%%% -*-BibTeX-*-
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%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "1.15",
%%% date = "20 October 2023",
%%% time = "17:36:12 MDT",
%%% filename = "ecp.bib",
%%% address = "University of Utah
%%% Department of Mathematics, 110 LCB
%%% 155 S 1400 E RM 233
%%% Salt Lake City, UT 84112-0090
%%% USA",
%%% telephone = "+1 801 581 5254",
%%% FAX = "+1 801 581 4148",
%%% URL = "https://www.math.utah.edu/~beebe",
%%% checksum = "09986 39096 177303 1736067",
%%% email = "beebe at math.utah.edu, beebe at acm.org,
%%% beebe at computer.org (Internet)",
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%%% Communications in Probability",
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%%% docstring = "This is a COMPLETE bibliography of
%%% publications in the open-source journal,
%%% Electronic Communications in Probability
%%% (CODEN none, ISSN 1083-589X, ISSN-L
%%% 1083-589X) published in collaboration with
%%% the Institute of Mathematical Statistics.
%%% Publication began at the University of
%%% Washington (Seattle, WA, USA) with volume 1,
%%% number 1, in 1996. There is only one volume
%%% per year, but articles are available online
%%% as soon as they have been accepted for
%%% publication.
%%%
%%% In 2016, journal hosting moved to Project
%%% Euclid.
%%%
%%% The journal has Web sites at
%%%
%%% https://projecteuclid.org/euclid.ecp
%%% http://ecp.ejpecp.org/
%%% http://www.math.washington.edu/~ejpecp/ECP/
%%%
%%% There is also a companion journal for longer
%%% articles; it is covered in ejp.bib.
%%%
%%% At version 1.15, the year coverage looked
%%% like this:
%%%
%%% 1996 ( 10) 2006 ( 34) 2016 ( 76)
%%% 1997 ( 8) 2007 ( 46) 2017 ( 60)
%%% 1998 ( 13) 2008 ( 59) 2018 ( 93)
%%% 1999 ( 17) 2009 ( 57) 2019 ( 74)
%%% 2000 ( 14) 2010 ( 51) 2020 ( 80)
%%% 2001 ( 15) 2011 ( 70) 2021 ( 73)
%%% 2002 ( 19) 2012 ( 63) 2022 ( 65)
%%% 2003 ( 21) 2013 ( 96) 2023 ( 15)
%%% 2004 ( 20) 2014 ( 87)
%%% 2005 ( 30) 2015 ( 95)
%%%
%%% Article: 1361
%%%
%%% Total entries: 1361
%%%
%%% Data for this bibliography have been derived
%%% primarily from data at the publisher Web
%%% site, with contributions from the BibNet
%%% Project and TeX User Group bibliography
%%% archives, and the MathSciNet and zbMATH
%%% databases.
%%%
%%% Numerous errors in the sources noted above
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%%% family name of the first author or editor,
%%% year is a 4-digit number, and abbrev is a
%%% 3-letter condensation of important title
%%% words. Citation tags were automatically
%%% generated by the biblabel software
%%% developed for the BibNet Project.
%%%
%%% In this bibliography, entries are sorted in
%%% publication order, with the help of
%%% ``bibsort -bypages''.
%%%
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%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|https://www.math.utah.edu/~beebe/|"}
%%% ====================================================================
%%% Journal abbreviations:
@String{j-ELECTRON-COMMUN-PROBAB = "Electronic Communications in Probability"}
%%% ====================================================================
%%% Bibliography entries, sorted in publication order with
%%% ``bibsort -byvolume'':
@Article{Kesten:1996:NCT,
author = "Harry Kesten",
title = "On the Non-Convexity of the Time Constant in
First-Passage Percolation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "1",
pages = "1:1--1:6",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v1-971",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60K35 (82B43)",
MRnumber = "1386288 (98c:60142)",
MRreviewer = "John C. Wierman",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/971",
abstract = "We give a counterexample to a
\url{http://www.ams.org/mathscinet-getitem?mr=33:6731}
conjecture of Hammersley and Welsh (1965) about the
convexity of the time constant in first-passage
percolation, as a functional on the space of
distribution functions. The present counterexample only
works for first-passage percolation on $ Z^d $ for $d$
large.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "First-passage percolation, time constant, convexity.",
}
@Article{Kwapien:1996:PCB,
author = "S. Kwapien and M. Pycia and W. Schachermayer",
title = "A Proof of a Conjecture of {Bobkov} and {Houdr{\'e}}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "1",
pages = "2:7--2:10",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v1-972",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60E05",
MRnumber = "1386289 (97c:60032)",
MRreviewer = "Christian Houdr{\'e}",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/972",
abstract = "S. G. Bobkov and C. Houdr{\'e} recently posed the
following question on the Internet
(\url{http://www.sad.princeton.edu/sad/sad15/8}Problem
posed in Stochastic Analysis Digest no. 15
(9/15/1995)): Let $ X, Y $ be symmetric i.i.d. random
variables such that\par
$$ P(|X + Y| / 2 \geq t) \leq P(|X| \geq t), $$
for each $ t > 0 $. Does it follow that $X$ has finite
second moment (which then easily implies that $X$ is
Gaussian)? In this note we give an affirmative answer
to this problem and present a proof. Using a different
method K. Oleszkiewicz has found another proof of this
conjecture, as well as further related results.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Gaussian distribution.",
}
@Article{Dembo:1996:MDM,
author = "Amir Dembo",
title = "Moderate Deviations for Martingales with Bounded
Jumps",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "1",
pages = "3:11--3:17",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v1-973",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60F10 (60E15 60F17 60G42 60G44)",
MRnumber = "1386290 (97k:60077)",
MRreviewer = "Anatolii A. Pukhal{\cprime}ski{\u\i}",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/973",
abstract = "We prove that the Moderate Deviation Principle (MDP)
holds for the trajectory of a locally square integrable
martingale with bounded jumps as soon as its quadratic
covariation, properly scaled, converges in probability
at an exponential rate. A consequence of this MDP is
the tightness of the method of bounded martingale
differences in the regime of moderate deviations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Moderate deviations, martingales, bounded martingale
differences.",
}
@Article{Werner:1996:BDE,
author = "Wendelin Werner",
title = "Bounds for Disconnection Exponents",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "1",
pages = "4:19--4:28",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v1-974",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J65",
MRnumber = "1386291 (97c:60206)",
MRreviewer = "Jean Bertoin",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/974",
abstract = "We slightly improve the upper bounds of disconnection
exponents for planar Brownian motion that we derived in
an earlier paper. We also give a proof of the lower
bound $ 1 / (2 \pi) $ for the disconnection exponent
for one path.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion, disconnection exponents",
}
@Article{Lawler:1996:DFP,
author = "Gregory Lawler",
title = "The dimension of the frontier of planar {Brownian}
motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "1",
pages = "5:29--5:47",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v1-975",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J65",
MRnumber = "1386292 (97g:60110)",
MRreviewer = "Paul McGill",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/975",
abstract = "Let $B$ be a two dimensional Brownian motion and let
the frontier of $ B[0, 1]$ be defined as the set of all
points in $ B[0, 1]$ that are in the closure of the
unbounded connected component of its complement. We
prove that the Hausdorff dimension of the frontier
equals $ 2 (1 - \alpha)$ where $ \alpha $ is an
exponent for Brownian motion called the two-sided
disconnection exponent. In particular, using an
estimate on $ \alpha $ due to Werner, the Hausdorff
dimension is greater than $ 1.015$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion, Hausdorff dimension, frontier, random
fractals",
}
@Article{Puckette:1996:SCD,
author = "Emily E. Puckette and Wendelin Werner",
title = "Simulations and Conjectures for Disconnection
Exponents",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "1",
pages = "6:49--6:64",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v1-976",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J65 (65C05)",
MRnumber = "1423905 (97k:60223)",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/976",
abstract = "Using Monte-Carlo simulations, we estimate numerically
disconnection exponents for planar Brownian motions.
These simulations tend to confirm conjectures by
Duplantier and Mandelbrot.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion, disconnection exponents",
}
@Article{Jansons:1996:END,
author = "Kalvis M. Jansons",
title = "Excursions Into a New Duality Relation for Diffusion
Processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "1",
pages = "7:65--7:69",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v1-977",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60K35 (60J60)",
MRnumber = "1423906 (97m:60149)",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/977",
abstract = "This work was motivated by the recent work by H.
Dette, J. Pitman and W. J. Studden on a new duality
relation for random walks. In this note we consider the
diffusion process limit of their result, and use the
alternative approach of Ito excursion theory. This
leads to a duality for Ito excursion rates.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Excursions, Diffusion Processes",
}
@Article{Benjamini:1996:PBM,
author = "Itai Benjamini and Oded Schramm",
title = "Percolation Beyond {$ \mathbf {Z}^d $}, Many Questions
And a Few Answers",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "1",
pages = "8:71--8:82",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v1-978",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60K35 (82B43)",
MRnumber = "1423907 (97j:60179)",
MRreviewer = "Olle H{\"a}ggstr{\"o}m",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/978",
abstract = "A comprehensive study of percolation in a more general
context than the usual $ Z^d $ setting is proposed,
with particular focus on Cayley graphs, almost
transitive graphs, and planar graphs. Results
concerning uniqueness of infinite clusters and
inequalities for the critical value $ p_c $ are given,
and a simple planar example exhibiting uniqueness and
non-uniqueness for different $ p > p_c $ is analyzed.
Numerous varied conjectures and problems are proposed,
with the hope of setting goals for future research in
percolation theory.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Percolation, criticality, planar graph, transitive
graph, isoperimetericinequality",
}
@Article{Dembo:1996:TAS,
author = "Amir Dembo and Ofer Zeitouni",
title = "Transportation Approach to Some Concentration
Inequalities in Product Spaces",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "1",
pages = "9:83--9:90",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v1-979",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60E15 (28A35)",
MRnumber = "1423908 (98d:60035)",
MRreviewer = "Iosif Pinelis",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/979",
abstract = "Using a transportation approach we prove that for
every probability measures $ P, Q_1, Q_2 $ on $
\Omega^N $ with $P$ a product measure there exist
r.c.p.d. $ \nu_j$ such that $ \int \nu_j (\cdot |x) d
P(x) = Q_j(\cdot)$ and\par
$$ \int d P (x) \int \frac {dP}{dQ_1} (y)^\beta \frac
{dP}{dQ_2} (z)^\beta (1 + \beta (1 - 2 \beta))^{f_N(x,
y, z)} d \nu_1 (y|x) d \nu_2 (z|x) \le 1 \;, $$
for every $ \beta \in (0, 1 / 2)$. Here $ f_N$ counts
the number of coordinates $k$ for which $ x_k \neq y_k$
and $ x_k \neq z_k$. In case $ Q_1 = Q_2$ one may take
$ \nu_1 = \nu_2$. In the special case of $ Q_j(\cdot) =
P(\cdot |A)$ we recover some of Talagrand's sharper
concentration inequalities in product spaces.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Concentration inequalities, product spaces,
transportation.",
}
@Article{Carmona:1996:SSO,
author = "Rene Carmona and Stanislav Grishin and Lin Xu and
Stanislav Molchanov",
title = "Surface Stretching for {Ornstein--Uhlenbeck} Velocity
Fields",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "2",
pages = "1:1--1:11",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v2-980",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/980",
abstract = "The present note deals with large time properties of
the Lagrangian trajectories of a turbulent flow in $
R^2 $ and $ R^3 $. We assume that the flow is driven by
an incompressible time-dependent random velocity field
with Gaussian statistics. We also assume that the field
is homogeneous in space and stationary and Markovian in
time. Such velocity fields can be viewed as (possibly
infinite dimensional) Ornstein--Uhlenbeck processes. In
d spatial dimensions we established the (strict)
positivity of the sum of the largest $ d - 1 $ Lyapunov
exponents. As a consequences of this result, we prove
the exponential stretching of surface areas (when $ d =
3$) and of curve lengths (when $ d = 2$.) This confirms
conjectures found in the theory of turbulent flows.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Diffusion Processes, Lyapunov Exponent, Stochastic
Flows.",
}
@Article{Carmona:1997:SSO,
author = "Rene A. Carmona and Stanislav Grishin and Lin Xu and
Stanislav Molchanov",
title = "Surface stretching for {Ornstein} {Uhlenbeck} velocity
fields",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "2",
pages = "1:1--1:11",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v2-980",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60H25 (60H30)",
MRnumber = "1448321 (99c:60132)",
MRreviewer = "Nariyuki Minami",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Roberts:1997:GEH,
author = "Gareth O. Roberts and Jeffrey S. Rosenthal",
title = "Geometric ergodicity and hybrid {Markov} chains",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "2",
pages = "2:13--2:25",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v2-981",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J35 (60F25 60J10)",
MRnumber = "1448322 (99b:60122)",
MRreviewer = "Esa Nummelin",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/981",
abstract = "Various notions of geometric ergodicity for Markov
chains on general state spaces exist. In this paper, we
review certain relations and implications among them.
We then apply these results to a collection of chains
commonly used in Markov chain Monte Carlo simulation
algorithms, the so-called hybrid chains. We prove that
under certain conditions, a hybrid chain will
{"inherit"} the geometric ergodicity of its constituent
parts.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Markov chain Monte Carlo, hybrid Monte Carlo,
geometric ergodicity, reversibility, spectral gap.",
}
@Article{Kiesel:1997:SLS,
author = "R{\"u}diger Kiesel",
title = "Strong laws and summability for sequences of {$ \phi
$}-mixing random variables in {Banach} spaces",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "2",
pages = "3:27--3:41",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v2-982",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60F15 (40A05 40J05 60B12)",
MRnumber = "1448323 (2000a:60057)",
MRreviewer = "A. Bozorgnia",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/982",
abstract = "In this note the almost sure convergence of
stationary, $ \varphi $-mixing sequences of random
variables with values in real, separable Banach spaces
according to summability methods is linked to the
fulfillment of a certain integrability condition
generalizing and extending the results for i.i.d.
sequences. Furthermore we give via Baum-Katz type
results an estimate for the rate of convergence in
these laws.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Strong Laws, $varphi$-mixing, Summability.",
}
@Article{Barlow:1997:PBT,
author = "Martin T. Barlow and Richard F. Bass and Krzysztof
Burdzy",
title = "Positivity of {Brownian} Transition Densities",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "2",
pages = "4:43--4:51",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v2-983",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J35 (60J65)",
MRnumber = "1484554 (99e:60166)",
MRreviewer = "Lo{\"{\i}}c Chaumont",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/983",
abstract = "Let $B$ be a Borel subset of $ R^d$ and let $ p(t, x,
y)$ be the transition densities of Brownian motion
killed on leaving $B$. Fix $x$ and $y$ in $B$. If $
p(t, x, y)$ is positive for one $t$, it is positive for
every value of $t$. Some related results are given.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Transition densities, Brownian motion, eigenvalue
expansion, fine topology, regular points.",
}
@Article{Jansons:1997:DTS,
author = "Kalvis M. Jansons",
title = "The Distribution of Time Spent by a Standard Excursion
Above a Given Level, with Applications to Ring Polymers
near a Discontinuity in Potential",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "2",
pages = "5:53--5:58",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v2-984",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J65",
MRnumber = "1484555 (98k:60141)",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/984",
abstract = "The law for the time $ \tau_a $ spent by a standard
Brownian excursion above a given level $ a > 0 $ is
found using Ito excursion theory. This is achieved by
conditioning the excursion to have exactly one mark of
an independent Poisson process. Various excursion rates
for excursions conditioned to have exactly $n$ marks
are also given in terms of generating functions. This
work has applications to the theory of ring polymers
and end-attached polymers near a discontinuity in
potential.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Standard Brownian Excursions, Brownian Bridges, Ring
Polymers, End-Attached Polymers.",
}
@Article{Kaj:1997:SAS,
author = "Ingemar Kaj and Serik Sagitov",
title = "Superprocess Approximation For a Spatially Homogeneous
Branching Walk",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "2",
pages = "6:59--6:70",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v2-985",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J85 (60J80)",
MRnumber = "1484556 (99a:60094)",
MRreviewer = "Luis G. Gorostiza",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/985",
abstract = "We present an alternative particle picture for
super-stable motion. It is based on a non-local
branching mechanism in discrete time and only trivial
space motion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Superprocess, critical branching walk, time-space-mass
scaling, integral equations.",
}
@Article{Capitaine:1997:MRS,
author = "Mireille Capitaine and Elton P. Hsu and Michel
Ledoux",
title = "Martingale Representation and a Simple Proof of
Logarithmic {Sobolev} Inequalities on Path Spaces",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "2",
pages = "7:71--7:81",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v2-986",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J65 (58D20 58G32 60B15 60D05 60H07)",
MRnumber = "1484557 (99b:60136)",
MRreviewer = "Shi Zan Fang",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/986",
abstract = "We show how the Clark-Ocone-Haussmann formula for
Brownian motion on a compact Riemannian manifold put
forward by S. Fang in his proof of the spectral gap
inequality for the Ornstein--Uhlenbeck operator on the
path space can yield in a very simple way the
logarithmic Sobolev inequality on the same space. By an
appropriate integration by parts formula the proof also
yields in the same way a logarithmic Sobolev inequality
for the path space equipped with a general diffusion
measure as long as the torsion of the corresponding
Riemannian connection satisfies Driver's total
antisymmetry condition.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Martingale representation, logarithmic Sobolev
inequality, Brownian motion, Riemannian manifold",
}
@Article{Baryshnikov:1997:WSG,
author = "Yuliy Baryshnikov",
title = "{Wiener} Soccer and Its Generalization",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "3",
pages = "1:1--1:11",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v3-987",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/987",
abstract = "The trajectory of the ball in a soccer game is
modelled by the Brownian motion on a cylinder, subject
to elastic reflections at the boundary points (as
proposed in [KPY]). The score is then the number of
windings of the trajectory around the cylinder. We
consider a generalization of this model to higher
genus, prove asymptotic normality of the score and
derive the covariance matrix. Further, we investigate
the inverse problem: to what extent the underlying
geometry can be reconstructed from the asymptotic
score.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Wiener Process, Brownian Motion.",
}
@Article{Baryshnikov:1998:WSG,
author = "Yuliy Baryshnikov",
title = "{Wiener} soccer and its generalization",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "3",
pages = "1--11",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v3-987",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J35 (60J65)",
MRnumber = "1492035 (99c:60158)",
MRreviewer = "Robert J. Adler",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Arcones:1998:LLN,
author = "Miguel A. Arcones",
title = "The Law of Large Numbers for {$U$}-statistics Under
Absolute Regularity",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "3",
pages = "2:13--2:19",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v3-988",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60F15",
MRnumber = "1624866 (99d:60038)",
MRreviewer = "Manfred Denker",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/988",
abstract = "We prove the law of large numbers for $U$-statistics
whose underlying sequence of random variables satisfies
an absolute regularity condition ($ \beta $-mixing
condition) under suboptimal conditions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Law of the large numbers, $U$-statistics, absolute
regularity.",
}
@Article{Evans:1998:EIS,
author = "Steven N. Evans and Yuval Peres",
title = "Eventual Intersection for Sequences of {L{\'e}vy}
Processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "3",
pages = "3:21--3:27",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v3-989",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J30 (60B15 60D05 60G17 60J45)",
MRnumber = "1625695 (99g:60130)",
MRreviewer = "Davar Khoshnevisan",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/989",
abstract = "Consider the events $ \{ F_n \cap \bigcup_{k = 1}^{n -
1} F_k = \emptyset \} $, $ n \in N $, where $ (F_n)_{n
= 1}^\infty $ is an i.i.d. sequence of stationary
random subsets of a compact group $G$. A plausible
conjecture is that these events will not occur
infinitely often with positive probability if $ P \{
F_i \cap F_j \ne \emptyset \mid F_j \} > 0$ a.s. for $
i \ne j$. We present a counterexample to show that this
condition is not sufficient, and give one that is. The
sufficient condition always holds when $ F_n = \{ X_t^n
: 0 \le t \le T \} $ is the range of a L{\'e}vy process
$ X^n$ on the $d$-dimensional torus with uniformly
distributed initial position and $ P \{ \exists 0 \le
s, t \le T : X_s^i = X_t^j \} > 0$ for $ i \ne j$. We
also establish an analogous result for the sequence of
graphs $ \{ (t, X_t^n) : 0 \le t \le T \} $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "L{\'e}vy process, hitting probability, range, graph,
random measure, random set, stationary",
}
@Article{Burdzy:1998:WCR,
author = "Krzysztof Burdzy and Zhen-Qing Chen",
title = "Weak Convergence of Reflecting {Brownian} Motions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "3",
pages = "4:29--4:33",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v3-990",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J65",
MRnumber = "1625707 (99d:60091)",
MRreviewer = "Youngmee Kwon",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/990",
abstract = "We show that if a sequence of domains $ D_k $
increases to a domain $D$ then the reflected Brownian
motions in $ D_k$'s converge to the reflected Brownian
motion in $D$, under mild technical assumptions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "reflected Brownian motion, weak convergence.",
}
@Article{Lawler:1998:LEW,
author = "Gregory F. Lawler",
title = "Loop-Erased Walks Intersect Infinitely Often in Four
Dimensions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "3",
pages = "5:35--5:42",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v3-991",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J15",
MRnumber = "1637969 (99e:60156)",
MRreviewer = "Thomas Polaski",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/991",
abstract = "In this short note we show that the paths two
independent loop-erased random walks in four dimensions
intersect infinitely often. We actually prove the
stronger result that the cut-points of the two walks
intersect infinitely often.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random Walks, Loop-Erased Walks, Intersections",
}
@Article{Thalmaier:1998:SRH,
author = "Anton Thalmaier",
title = "Some Remarks on the Heat Flow for Functions and
Forms",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "3",
pages = "6:43--6:49",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v3-992",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "58G32 (58G11 60G44)",
MRnumber = "1637977 (99i:58157)",
MRreviewer = "Elton Pei Hsu",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/992",
abstract = "This note is concerned with the differentiation of
heat semigroups on Riemannian manifolds. In particular,
the relation $ d P_t f = P_t d f $ is investigated for
the semigroup generated by the Laplacian with Dirichlet
boundary conditions. By means of elementary martingale
arguments it is shown that well-known properties which
hold on complete Riemannian manifolds fail if the
manifold is only BM-complete. In general, even if $M$
is flat and $f$ smooth of compact support, $ \Vert d
P_t f \Vert_\infty $ cannot be estimated on compact
time intervals in terms of $f$ or $ d f$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Heat semigroup, heat equation, Brownian motion, damped
parallel translation, Ricci curvature.",
}
@Article{Fargason:1998:PDB,
author = "Chad Fargason",
title = "Percolation dimension of {Brownian} motion in {$
\mathbf {R}^3 $}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "3",
pages = "7:51--7:63",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v3-993",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J65",
MRnumber = "1641070 (99g:60149)",
MRreviewer = "Davar Khoshnevisan",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/993",
abstract = "Let $ B(t) $ be a Brownian motion in $ R^3 $. A {\em
subpath\/} of the Brownian path $ B[0, 1] $ is a
continuous curve $ \gamma (t) $, where $ \gamma [0, 1]
\subseteq B[0, 1] $ , $ \gamma (0) = B(0) $, and $
\gamma (1) = B(1) $. It is well-known that any subset
$S$ of a Brownian path must have Hausdorff dimension $
\text {dim} (S) \leq 2.$ This paper proves that with
probability one there exist subpaths of $ B[0, 1]$ with
Hausdorff dimension strictly less than 2. Thus the
percolation dimension of Brownian motion in $ R^3$ is
strictly less than 2.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Percolation dimension, boundary dimension,
intersection exponent",
}
@Article{Rincon:1998:EDD,
author = "L. A. Rincon",
title = "Estimates for the Derivative of Diffusion Semigroups",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "3",
pages = "8:65--8:74",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v3-994",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J60 (47D07 60H10)",
MRnumber = "1641074 (99g:60144)",
MRreviewer = "Ren Ming Song",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/994",
abstract = "Let $ \{ P_t \}_{t \ge 0} $ be the transition
semigroup of a diffusion process. It is known that $
P_t $ sends continuous functions into differentiable
functions so we can write $ D P_t f $. But what happens
with this derivative when $ t \to 0 $ and $ P_0 f = f $
is only continuous?. We give estimates for the supremum
norm of the Frechet derivative of the semigroups
associated with the operators $ {\cal A} + V $ and $
{\cal A} + Z \cdot \nabla $ where $ {\cal A} $ is the
generator of a diffusion process, $V$ is a potential
and $Z$ is a vector field.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Diffusion Semigroups, Diffusion Processes, Stochastic
Differential Equations.",
xxtitle = "Estimates for the derivatives of diffusion
semigroups",
}
@Article{Ryznar:1998:UUB,
author = "Micha{\l} Ryznar and Tomasz {\.Z}ak",
title = "Uniform Upper Bound for a Stable Measure of a Small
Ball",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "3",
pages = "9:75--9:78",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v3-995",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60E07 (46B20 46G12)",
MRnumber = "1645592 (99g:60034)",
MRreviewer = "Aleksandr Koldobsky",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/995",
abstract = "P. Hitczenko, S. Kwapien, W. N. Li, G. Schechtman, T.
Schlumprecht and J. Zinn stated the following
conjecture. Let $ \mu $ be a symmetric $ \alpha
$-stable measure on a separable Banach space and $B$ a
centered ball such that $ \mu (B) \le b$. Then there
exists a constant $ R(b)$, depending only on $b$, such
that $ \mu (t B) \le R(b)t \mu (B)$ for all $ 0 < t <
1$. We prove that the above inequality holds but the
constant $R$ must depend also on $ \alpha $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "stable measure, small ball",
}
@Article{Aldous:1998:BEC,
author = "David J. Aldous",
title = "{Brownian} Excursion Conditioned on Its Local Time",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "3",
pages = "10:79--10:90",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v3-996",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J55 (60J65)",
MRnumber = "1650567 (99m:60115)",
MRreviewer = "Ingemar Kaj",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/996",
abstract = "For a function $ \ell $ satisfying suitable
integrability (but not continuity) requirements, we
construct a process $ (B^\ell_u, 0 \leq u \leq 1) $
interpretable as Brownian excursion conditioned to have
local time $ \ell (\cdot) $ at time $1$. The
construction is achieved by first defining a
non-homogeneous version of Kingman's coalescent and
then applying the general theory in Aldous (1993)
relating excursion-type processes to continuum random
trees. This complements work of Warren and Yor (1997)
on the Brownian burglar.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian excursion, continuum random tree, Kingman's
coalescent, local time.",
}
@Article{Marchal:1998:BBT,
author = "Philippe Marchal",
title = "The Best Bounds in a Theorem of {Russell Lyons}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "3",
pages = "11:91--11:94",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v3-997",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60K35 (05C05)",
MRnumber = "1650563 (99j:60156)",
MRreviewer = "Wolfgang Woess",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/997",
abstract = "We sharpen a bound in a theorem of Russell Lyons for
percolation on a tree and associated random walk.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random Walks, Percolation, Tree.",
}
@Article{Carmona:1998:FBM,
author = "Philippe Carmona and Laure Coutin",
title = "Fractional {Brownian} Motion and the {Markov}
Property",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "3",
pages = "12:95--12:107",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v3-998",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60H35 (65C50)",
MRnumber = "1658690 (2000b:60163)",
MRreviewer = "Corinne Berzin",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/998",
abstract = "Fractional Brownian motion belongs to a class of long
memory Gaussian processes that can be represented as
linear functionals of an infinite dimensional Markov
process. This leads naturally to:\par
\begin{itemize} \item An efficient algorithm to
approximate the process. \item An ergodic theorem which
applies to functionals of the type\par
$$ \int_0^t \phi (V_h(s)), d s \quad {\rm where~}
\quad V_h(s) = \int_0^s h(s - u), d B_u. $$
\end{itemize}
where $B$ is a real Brownian motion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Gaussian processes, Markov Processes, Numerical
Approximation, Ergodic Theorem.",
}
@Article{Handa:1998:LBT,
author = "Kenji Handa",
title = "A Lower Bound for Time Correlation of Lattice Gases",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "1:1--1:8",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-999",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/999",
abstract = "The lattice gas model in equilibrium is considered. We
give a lower bound of the density-density time
correlation for large time, which involves the bulk
diffusion matrix in a physically natural way.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Lattice gas models, correlation function, the bulk
diffusion matrix.",
}
@Article{Handa:1999:LBT,
author = "Kenji Handa",
title = "A lower bound for time correlation of lattice gases",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "1--8",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-999",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "82C20 (60K35 82C22)",
MRnumber = "1691652 (2000g:82020)",
MRreviewer = "Raphael Lefevere",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Hooghiemstra:1999:OTB,
author = "Gerard Hooghiemstra",
title = "On the Occupation Time of {Brownian} Excursion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "8:61--8:64",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-1006",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J65",
MRnumber = "1711595 (2001h:60144)",
MRreviewer = "Robert J. Adler",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1006",
abstract = "Recently, Kalvin M. Jansons derived in an elegant way
the Laplace transform of the time spent by an excursion
above a given level $ a > 0 $. This result can also be
derived from previous work of the author on the
occupation time of the excursion in the interval $ (a,
a + b] $, by sending $ b \to \infty $. Several
alternative derivations are included.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian excursion, occupation time.",
}
@Article{Evans:1999:IES,
author = "Steven N. Evans and Xiaowen Zhou",
title = "Identifiability of Exchangeable Sequences with
Identically Distributed Partial Sums",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "2:9--2:13",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-1000",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60G09",
MRnumber = "1691653 (2000e:60055)",
MRreviewer = "N. C. Weber",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1000",
abstract = "Consider two exchangeable sequences $ (X_k)_{k \in N}
$ and $ (\hat {X}_k)_{k \in N} $ with the property that
$ S_n \equiv \sum_{k = 1}^n X_k $ and $ \hat {S}_n
\equiv \sum_{k = 1}^n \hat {X}_k $ have the same
distribution for all $ n \in N $. David Aldous posed
the following question. Does this imply that the two
exchangeable sequences have the same joint
distributions? We give an example that shows the answer
to Aldous' question is, in general, in the negative. On
the other hand, we show that the joint distributions of
an exchangeable sequence can be recovered from the
distributions of its partial sums if the sequence is a
countable mixture of i.i.d. sequences that are either
nonnegative or have finite moment generating functions
in some common neighbourhood of zero.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "exchangeability, de Finetti's theorem, characteristics
function, Laplace transform, moment generating
function",
}
@Article{Matsumoto:1999:SCP,
author = "Hiroyuki Matsumoto and Marc Yor",
title = "Some Changes of Probabilities Related to a Geometric
{Brownian} Motion Version of {Pitman}'s {$ 2 M - X $}
Theorem",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "3:15--3:23",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-1001",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J60 (60J65)",
MRnumber = "1703607 (2000e:60130)",
MRreviewer = "F. B. Knight",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1001",
abstract = "Rogers-Pitman have shown that the sum of the absolute
value of $ B^{(\mu)} $, Brownian motion with constant
drift $ \mu $, and its local time $ L^{(\mu)} $ is a
diffusion $ R^{(\mu)} $. We exploit the intertwining
relation between $ B^{(\mu)} $ and $ R^{(\mu)} $ to
show that the same addition operation performed on a
one-parameter family of diffusions $ {X^{(\alpha,
\mu)}}_{\alpha \in {\mathbf R}_+} $ yields the same
diffusion $ R^{(\mu)} $. Recently we obtained an
exponential analogue of the Rogers-Pitman result. Here
we exploit again the corresponding intertwining
relationship to yield a one-parameter family extension
of our result.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Diffusion Process, Geometric Brownian Motion, Markov
Intertwining Kernel, (strict) Local Martingale,
Explosion.",
}
@Article{Warren:1999:RDA,
author = "Jon Warren",
title = "On a Result of {David Aldous} Concerning the Trees in
a Conditioned Excursion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "4:25--4:29",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-1002",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J55",
MRnumber = "1703608 (2000f:60121)",
MRreviewer = "David J. Aldous",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1002",
abstract = "The law of a random tree constructed within a Brownian
excursion is calculated conditional on knowing the
occupation measure of the excursion. In previous work
David Aldous has used random walk approximations to
obtain this result. Here it is deduced from Le Gall's
description of the tree in the unconditioned
excursion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian excursion, random tree, local time.",
}
@Article{Bertoin:1999:CBP,
author = "Jean Bertoin and Jim Pitman and Juan {Ruiz de
Chavez}",
title = "Constructions of a {Brownian} Path With a Given
Minimum",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "5:31--5:37",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-1003",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J65 (60G17)",
MRnumber = "1703609 (2000j:60097)",
MRreviewer = "Paul McGill",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1003",
abstract = "We construct a Brownian path conditioned on its
minimum value over a fixed time interval by a simple
transformation of a Brownian bridge.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Conditioned Brownian motion, path transformations",
}
@Article{Schramm:1999:TCH,
author = "Oded Schramm and Boris Tsirelson",
title = "Trees, Not Cubes: Hypercontractivity, Cosiness, and
Noise Stability",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "6:39--6:49",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-1004",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J10 (05C05 42C10 46E39)",
MRnumber = "1711603 (2000k:60143)",
MRreviewer = "Laurent Miclo",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1004",
abstract = "Noise sensitivity of functions on the leaves of a
binary tree is studied, and a hypercontractive
inequality is obtained. We deduce that the spider walk
is not noise stable.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "hypercontractivity, cosiness, noise stability, noise
sensitivity",
}
@Article{Lindvall:1999:STS,
author = "Torgny Lindvall",
title = "On {Strassen}'s Theorem on Stochastic Domination",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "7:51--7:59",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-1005",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60B05 (60E15 60J05)",
MRnumber = "1711599 (2000k:60006)",
MRreviewer = "George L. O'Brien",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1005",
abstract = "The purpose of this note is to make available a
reasonably complete and straightforward proof of
Strassen's theorem on stochastic domination, and to
draw attention to the original paper. We also point out
that the maximal possible value of $ P(Z = Z') $ is
actually not reduced by the requirement $ Z \leq Z' $.
Here, $ Z, Z' $ are stochastic elements that Strassen's
theorem states exist under a stochastic domination
condition. The consequence of that observation to
stochastically monotone Markov chains is pointed out.
Usually the theorem is formulated with the assumption
that $ \leq $ is a partial ordering; the proof reveals
that a pre-ordering suffices.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Strassen's theorem, coupling, pre-ordering, maximal
diagonal probability",
}
@Article{Li:1999:RPF,
author = "Zenghu Li and Tokuzo Shiga and Lihua Yao",
title = "A Reversibility Problem for {Fleming--Viot}
Processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "9:65--9:76",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-1007",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60G57 (60J60)",
MRnumber = "1711591 (2001e:60097)",
MRreviewer = "Sylvie Roelly",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1007",
abstract = "Fleming--Viot processes incorporating mutation and
selection are considered. It is well-known that if the
mutation factor is of uniform type, the process has a
reversible stationary distribution, and it has been an
open problem to characterize the class of the processes
that have reversible stationary distributions. This
paper proves that if a Fleming--Viot process has a
reversible stationary distribution, then the associated
mutation operator is of uniform type.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Fleming--Viot processes, measure-valued diffusion,
reversibility, Dirichlet space",
}
@Article{Lewis:1999:CM,
author = "Thomas M. Lewis and Geoffrey Pritchard",
title = "Correlation Measures",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "10:77--10:85",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-1008",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60E15",
MRnumber = "1716783 (2000j:60023)",
MRreviewer = "Christian Houdr{\'e}",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1008",
abstract = "We study a class of Borel probability measures, called
correlation measures. Our results are of two types:
first, we give explicit constructions of non-trivial
correlation measures; second, we examine some of the
properties of the set of correlation measures. In
particular, we show that this set of measures has a
convexity property. Our work is related to the
so-called Gaussian correlation conjecture.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "correlation measures, Gaussian correlation
inequality",
}
@Article{Guillotin:1999:EOM,
author = "Nadine Guillotin",
title = "Edge Occupation Measure for a Reversible {Markov}
Chain",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "11:87--11:90",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-1009",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60J10 (60F05 60F10)",
MRnumber = "1741735 (2001g:60169)",
MRreviewer = "Wolfgang K{\"o}nig",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1009",
abstract = "In this note, we study the Gaussian fluctuations of
the edge occupation measure for a reversible Markov
chain and give a nice description of the covariance
matrix. Then we give some large deviations results
concerning this occupation measure.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Markov Chain, Limit theorems, Large deviations
principle",
}
@Article{Cranston:1999:LEI,
author = "Michael Cranston and Michael Scheutzow and David
Steinsaltz",
title = "Linear Expansion of Isotropic {Brownian} Flows",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "12:91--12:101",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-1010",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60H15 (60J65)",
MRnumber = "1741738 (2001d:60068)",
MRreviewer = "R{\'e}mi L{\'e}andre",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1010",
abstract = "We consider an isotropic Brownian flow on $ R^d $ for
$ d \geq 2 $ with a positive Lyapunov exponent, and
show that any nontrivial connected set almost surely
contains points whose distance from the origin under
the flow grows linearly with time. The speed is bounded
below by a fixed constant, which may be computed from
the covariance tensor of the flow. This complements
earlier work, which showed that stochastic flows with
bounded local characteristics and zero drift cannot
grow at a linear rate faster than linear.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stochastic flows, Brownian flows, stochastic
differential equations, martingale fields, Lyapunov
exponents",
}
@Article{Csaki:1999:CEB,
author = "Endre Cs{\'a}ki and Davar Khoshnevisan and Zhan Shi",
title = "Capacity Estimates, Boundary Crossings and the
{Ornstein--Uhlenbeck} Process in {Wiener} Space",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "13:103--13:109",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-1011",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60G15 (60G40 60G60 60J45 60J65)",
MRnumber = "1741736 (2001g:60083)",
MRreviewer = "Shi Zan Fang",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1011",
abstract = "Let $ T_1 $ denote the first passage time to 1 of a
standard Brownian motion. It is well known that as $
\lambda $ goes to infinity, $ P \{ T_1 > \lambda \} $
goes to zero at rate $ c \lambda^{-1 / 2} $, where $c$
equals $ (2 / \pi)^{1 / 2}$. The goal of this note is
to establish a quantitative, infinite dimensional
version of this result. Namely, we will prove the
existence of positive and finite constants $ K_1$ and $
K_2$, such that for all $ \lambda > e^e$, \par
$$ K_1 \lambda^{-1 / 2} \leq \text {Cap} \{ T_1 >
\lambda \} \leq K_2 \lambda^{-1 / 2} \log^3 (\lambda)
\cdot \log \log (\lambda), $$
where `$ \log $' denotes the natural logarithm, and $
\text {Cap}$ is the Fukushima-Malliavin capacity on the
space of continuous functions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Capacity on Wiener space, quasi-sure analysis,
Ornstein--Uhlenbeck process, Brownian sheet.",
}
@Article{Li:1999:GCI,
author = "Wenbo V. Li",
title = "A {Gaussian} Correlation Inequality and its
Applications to Small Ball Probabilities",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "4",
pages = "14:111--14:118",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v4-1012",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60G15 (60E15)",
MRnumber = "1741737 (2001j:60074)",
MRreviewer = "Qi Man Shao",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1012",
abstract = "We present a Gaussian correlation inequality which is
closely related to a result of Schechtman, Schlumprecht
and Zinn (1998) on the well-known Gaussian correlation
conjecture. The usefulness of the inequality is
demonstrated by several important applications to the
estimates of small ball probability.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Small ball probabilities, Gaussian correlation
inequality",
}
@Article{Schweinsberg:1999:NSC,
author = "Jason Schweinsberg",
title = "A Necessary and Sufficient Condition for the
Lambda-Coalescent to Come Down from Infinity",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "1:1--1:11",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1013",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1013",
abstract = "Let $ \Pi_{\infty } $ be the standard $ \Lambda
$-coalescent of Pitman, which is defined so that $
\Pi_{\infty }(0)$ is the partition of the positive
integers into singletons, and, if $ \Pi_n$ denotes the
restriction of $ \Pi_{\infty }$ to $ \{ 1, \ldots, n \}
$, then whenever $ \Pi_n(t)$ has $b$ blocks, each
$k$-tuple of blocks is merging to form a single block
at the rate $ \lambda_{b, k}$, where $ \lambda_{b, k} =
\int_0^1 x^{k - 2} (1 - x)^{b - k} \Lambda (d x)$ for
some finite measure $ \Lambda $. We give a necessary
and sufficient condition for the $ \Lambda $-coalescent
to ``come down from infinity'', which means that the
partition $ \Pi_{\infty }(t)$ almost surely consists of
only finitely many blocks for all $ t > 0$. We then
show how this result applies to some particular
families of $ \Lambda $-coalescents.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "coalescent, Kochen-Stone Lemma",
}
@Article{Limic:1999:BLP,
author = "Vlada Limic",
title = "On the Behavior of {LIFO} Preemptive Resume Queues in
Heavy Traffic",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "2:13--2:27",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1014",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1014",
abstract = "This paper studies heavy traffic behavior of a G/G/1
last-in-first-out (LIFO) preemptive resume queue, by
extending the techniques developed in Limic (1999). The
queue length process exhibits a perhaps unexpected
heavy traffic behavior. The diffusion limit depends on
the type of arrivals (and services) in a fairly
intricate way, related to the Wiener-Hopf factorization
for random walks.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "LIFO queue, heavy traffic, measure-valued process,
branching, feedback, renewal, Wiener-Hopf
factorization",
}
@Article{Marchal:1999:LER,
author = "Philippe Marchal",
title = "Loop-Erased Random Walks, Spanning Trees and
{Hamiltonian} Cycles",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "4:39--4:50",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1016",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1016",
abstract = "We establish a formula for the distribution of
loop-erased random walks at certain random times.
Several classical results on spanning trees, including
Wilson's algorithm, follow easily, as well as a method
to construct random Hamiltonian cycles.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Loop-erased random walk, spanning tree, Wilson's
algorithm",
}
@Article{Telcs:2000:TPE,
author = "Andras Telcs",
title = "Transition Probability Estimates for Reversible
{Markov} Chains",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "3:29--3:37",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1015",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1015",
abstract = "This paper provides transition probability estimates
of transient reversible Markov chains. The key
condition of the result is the spatial symmetry and
polynomial decay of the Green's function of the
chain.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random walks, reversible Markov chains, fractals,
dimensions",
}
@Article{Bertoin:2000:CMC,
author = "Jean Bertoin",
title = "The Convex Minorant of the {Cauchy} Process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "5:51--5:55",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1017",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1017",
abstract = "We determine the law of the convex minorant $ (M_s, s
\in [0, 1]) $ of a real-valued Cauchy process on the
unit time interval, in terms of the gamma process. In
particular, this enables us to deduce that the paths of
$M$ have a continuous derivative, and that the support
of the Stieltjes measure $ d M'$ has logarithmic
dimension one.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Cauchy process, Gamma process, convex minorant",
}
@Article{Barlow:2000:VSB,
author = "Martin Barlow and Krzysztof Burdzy and Haya Kaspi and
Avi Mandelbaum",
title = "Variably Skewed {Brownian} Motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "6:57--6:66",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1018",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1018",
abstract = "Given a standard Brownian motion $B$, we show that the
equation\par
$$ X_t = x_0 + B_t + \beta (L_t^X), t \geq 0, $$
has a unique strong solution $X$. Here $ L^X$ is the
symmetric local time of $X$ at $0$, and $ \beta $ is a
given differentiable function with $ \beta (0) = 0$,
whose derivative is always in $ ( - 1, 1)$. For a
linear function $ \beta $, the solution is the familiar
skew Brownian motion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Skew Brownian motion, Brownian motion, stochastic
differential equation, local time",
}
@Article{Angel:2000:LWS,
author = "Omer Angel and Itai Benjamini and Yuval Peres",
title = "A Large {Wiener} Sausage from Crumbs",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "7:67--7:71",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1019",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1019",
abstract = "Let $ B(t) $ denote Brownian motion in $ R^d $. It is
a classical fact that for any Borel set $A$ in $ R^d$,
the volume $ V_1 (A)$ of the Wiener sausage $ B[0, 1] +
A$ has nonzero expectation iff $A$ is nonpolar. We show
that for any nonpolar $A$, the random variable $ V_1
(A)$ is unbounded.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion, capacity, polar set, Wiener
sausage.",
}
@Article{Sepanski:2000:WLL,
author = "Steven Sepanski and Zhidong Pan",
title = "A Weak Law of Large Numbers for the Sample Covariance
Matrix",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "8:73--8:76",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1020",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1020",
abstract = "In this article we consider the sample covariance
matrix formed from a sequence of independent and
identically distributed random vectors from the
generalized domain of attraction of the multivariate
normal law. We show that this sample covariance matrix,
appropriately normalized by a nonrandom sequence of
linear operators, converges in probability to the
identity matrix.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Law of large numbers, affine normalization, sample
covariance, central limit theorem, domain of
attraction, generalized domain of attraction,
multivariate t statistic",
}
@Article{Fill:2000:CSF,
author = "James Fill and Svante Janson",
title = "A Characterization of the Set of Fixed Points of the
{Quicksort} Transformation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "9:77--9:84",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1021",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1021",
abstract = "The limiting distribution $ \mu $ of the normalized
number of key comparisons required by the Quicksort
sorting algorithm is known to be the unique fixed point
of a certain distributional transformation $T$ -
unique, that is, subject to the constraints of zero
mean and finite variance. We show that a distribution
is a fixed point of $T$ if and only if it is the
convolution of $ \mu $ with a Cauchy distribution of
arbitrary center and scale. In particular, therefore, $
\mu $ is the unique fixed point of $T$ having zero
mean.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Quicksort, fixed point, characteristic function,
smoothing transformation, domain of attraction,
coupling, integral equation",
}
@Article{Jonasson:2000:CTP,
author = "Johan Jonasson and Oded Schramm",
title = "On the Cover Time of Planar Graphs",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "10:85--10:90",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1022",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1022",
abstract = "The cover time of a finite connected graph is the
expected number of steps needed for a simple random
walk on the graph to visit all the vertices. It is
known that the cover time on any $n$-vertex, connected
graph is at least $ \bigl (1 + o(1) \bigr)n \log n$ and
at most $ \bigl (1 + o(1) \bigr) \frac {4}{27}n^3$.
This paper proves that for bounded-degree planar graphs
the cover time is at least $ c n(\log n)^2$, and at
most $ 6 n^2$, where $c$ is a positive constant
depending only on the maximal degree of the graph. The
lower bound is established via use of circle
packings.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "effective resistance, commute time, hitting time,
difference time, circle packing, triangulation",
}
@Article{Fitzsimmons:2000:SFM,
author = "P. Fitzsimmons",
title = "Strict Fine Maxima",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "11:91--11:94",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1023",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1023",
abstract = "We provide a simple probabilistic proof of a result of
J. Kr{\'a}l and I. Netuka: If $f$ is a measurable
real-valued function on $ \mathbb {R}^d$ ($ d > 1$)
then the set of points at which $f$ has a strict {\em
fine\/} local maximum value is polar.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion, fine topology, local maxima, optional
projection.",
}
@Article{Devroye:2000:PSQ,
author = "Luc Devroye and James Fill and Ralph Neininger",
title = "Perfect Simulation from the {Quicksort} Limit
Distribution",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "12:95--12:99",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1024",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://ecp.ejpecp.org/article/view/1024",
abstract = "The weak limit of the normalized number of comparisons
needed by the Quicksort algorithm to sort $n$ randomly
permuted items is known to be determined implicitly by
a distributional fixed-point equation. We give an
algorithm for perfect random variate generation from
this distribution.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Quicksort, random variate generation, simulation,
perfect simulation, rejection method, Monte Carlo
method, fixed-point equation",
}
@Article{Briand:2000:CCT,
author = "Philippe Briand and Fran{\c{c}}ois Coquet and Ying Hu
and Jean M{\'e}min and Shige Peng",
title = "A Converse Comparison Theorem for {BSDEs} and Related
Properties of $g$-Expectation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "13:101--13:117",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1025",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1025",
abstract = "In [1], Z. Chen proved that, if for each terminal
condition $ \xi $, the solution of the BSDE associated
to the standard parameter $ (\xi, g_1) $ is equal at
time $ t = 0 $ to the solution of the BSDE associated
to $ (\xi, g_2) $ then we must have $ g_1 \equiv g_2 $.
This result yields a natural question: what happens in
the case of an inequality in place of an equality? In
this paper, we try to investigate this question and we
prove some properties of ``$g$-expectation'', notion
introduced by S. Peng in [8].",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Backward stochastic differential equations, comparison
theorem.",
}
@Article{Guionnet:2000:CSM,
author = "Alice Guionnet and Ofer Zeitouni",
title = "Concentration of the Spectral Measure for Large
Matrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "14:119--14:136",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1026",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1026",
abstract = "We derive concentration inequalities for functions of
the empirical measure of eigenvalues for large, random,
self adjoint matrices, with not necessarily Gaussian
entries. The results presented apply in particular to
non-Gaussian Wigner and Wishart matrices. We also
provide concentration bounds for non commutative
functionals of random matrices.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random Matrices, Concentration inequalities,
non-commutative functionals.",
}
@Article{Kuznetsov:2000:USG,
author = "Sergei Kuznetsov",
title = "On Uniqueness of a Solution of {$ L u = u^\alpha $}
with Given Trace",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "15:137--15:147",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1027",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1027",
abstract = "A boundary trace $ (\Gamma, \nu) $ of a solution of $
\Delta u = u^\alpha $ in a bounded smooth domain in $
\mathbb {R}^d $ was first constructed by Le Gall
\cite{LGOne} who described all possible traces for $
\alpha = 2, d = 2 $ in which case a solution is defined
uniquely by its trace. In a number of publications,
Marcus, V{\'e}ron, Dynkin and Kuznetsov gave analytic
and probabilistic generalization of the concept of
trace to the case of arbitrary $ \alpha > 1, d \ge 1 $.
However, it was shown by Le Gall that the trace, in
general, does not define a solution uniquely in case $
d \ge (\alpha + 1) / (\alpha - 1) $. He offered a
sufficient condition for the uniqueness and conjectured
that a uniqueness should be valid if the singular part
$ \Gamma $ of the trace coincides with the set of all
explosion points of the measure $ \nu $. Here, we
establish a necessary condition for the uniqueness
which implies a negative answer to the above
conjecture.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "superdiffusion, moderate solutions, sigma-moderate
solutions, stochastic boundary values, trace of a
solution, explosion points.",
}
@Article{Simon:2000:SME,
author = "Thomas Simon",
title = "Support of a {Marcus} equation in Dimension $1$",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "16:149--16:157",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1028",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1028",
abstract = "The purpose of this note is to give a support theorem
in the Skorohod space for a one-dimensional Marcus
differential equation driven by a L{\'e}vy process,
without any assumption on the latter. We also give a
criterion ensuring that the support of the equation is
the whole Skorohod space. This improves, in dimension
1, a result of H. Kunita.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Fagnola:2000:MSQ,
author = "Franco Fagnola and Stephen Wills",
title = "Mild Solutions of Quantum Stochastic Differential
Equations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "5",
pages = "17:158--17:171",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v5-1029",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1029",
abstract = "We introduce the concept of a mild solution for the
right Hudson-Parthasarathy quantum stochastic
differential equation, prove existence and uniqueness
results, and show the correspondence between our
definition and similar ideas in the theory of classical
stochastic differential equations. The conditions that
a process must satisfy in order for it to be a mild
solution are shown to be strictly weaker than those for
it to be a strong solution by exhibiting a class of
coefficient matrices for which a mild unitary solution
can be found, but for which no strong solution
exists.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Quantum stochastic, stochastic differential equation,
mild solution",
}
@Article{Briand:2001:DTT,
author = "Philippe Briand and Bernard Delyon and Jean
M{\'e}min",
title = "{Donsker}-Type Theorem for {BSDEs}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "6",
pages = "1:1--1:14",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v6-1030",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1030",
abstract = "This paper is devoted to the proof of Donsker's
theorem for backward stochastic differential equations
(BSDEs for short). The main objective is to give a
simple method to discretize in time a BSDE. Our
approach is based upon the notion of ``convergence of
filtrations'' and covers the case of a $ (y,
z)$-dependent generator.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Backward stochastic differential equation (BSDE),
stability of BSDEs, weak convergence of filtrations,
discretization.",
}
@Article{Marcus:2001:NID,
author = "Michael Marcus and Jan Rosinski",
title = "{$ L^1 $}-Norm of Infinitely Divisible Random Vectors
and Certain Stochastic Integrals",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "6",
pages = "2:15--2:29",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v6-1031",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1031",
abstract = "Equivalent upper and lower bounds for the $ L^1 $ norm
of Hilbert space valued infinitely divisible random
variables are obtained and used to find bounds for
different types of stochastic integrals.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Infinitely divisible random variables, stochastic
integrals",
}
@Article{Atar:2001:BDP,
author = "Rami Atar and Siva Athreya and Min Kang",
title = "Ballistic Deposition on a Planar Strip",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "6",
pages = "3:31--3:38",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v6-1032",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1032",
abstract = "We consider ballistic diffusion limited aggregation on
a finite strip $ [0, L - 1] $ times $ \mathbb {Z}_+ $
in $ \mathbb {Z}^2 $ for some $L$ in $ \mathbb {Z}_+$.
We provide numerical bounds on the growth in the height
process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Ballistic, Deposition, Diffusion Limited
Aggregation.",
}
@Article{Giacomin:2001:RTS,
author = "Giambattista Giacomin and Gustavo Posta",
title = "On Recurrent and Transient Sets of Inhomogeneous
Symmetric Random Walks",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "6",
pages = "4:39--4:53",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v6-1033",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1033",
abstract = "We consider a continuous time random walk on the
$d$-dimensional lattice $ \mathbb {Z}^d$: the jump
rates are time dependent, but symmetric and strongly
elliptic with ellipticity constants independent of
time. We investigate the implications of heat kernel
estimates on recurrence-transience properties of the
walk and we give conditions for recurrence as well as
for transience: we give applications of these
conditions and discuss them in relation with the
(optimal) Wiener test available in the time independent
context. Our approach relies on estimates on the time
spent by the walk in a set and on a 0-1 law. We show
also that, still via heat kernel estimates, one can
avoid using a 0-1 law, achieving this way quantitative
estimates on more general hitting probabilities.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Inhomogeneous Symmetric Random Walks, Heat Kernel
Estimates, Recurrence-Transience, Hitting
Probabilities, Wiener test, Paley-Zygmund inequality",
}
@Article{Panchenko:2001:NTC,
author = "Dmitriy Panchenko",
title = "A Note on {Talagrand}'s Concentration Inequality",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "6",
pages = "5:55--5:65",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v6-1034",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1034",
abstract = "In this paper we revisit Talagrand's proof of
concentration inequality for empirical processes. We
give a different proof of the main technical lemma that
guarantees the existence of a certain kernel. Moreover,
we generalize the result of Talagrand to a family of
kernels which in one particular case allows us to
produce the Poissonian bound without using the
truncation argument. We also give some examples of
applications of the abstract concentration inequality
to empirical processes that demonstrate some
interesting properties of Talagrand's kernel method.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Concentration of measure, empirical processes",
}
@Article{Swart:2001:DSW,
author = "Jan Swart",
title = "A {$2$}-Dimensional {SDE} Whose Solutions are Not
Unique",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "6",
pages = "6:67--6:71",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v6-1035",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1035",
abstract = "In 1971, Yamada and Watanabe showed that pathwise
uniqueness holds for the SDE $ d X = \sigma (X)d B $
when sigma takes values in the n-by-m matrices and
satisfies $ | \sigma (x) - \sigma (y)| < |x - y| \log
(1 / |x - y|)^{1 / 2} $. When $ n = m = 2 $ and $
\sigma $ is of the form $ \sigma_{ij}(x) =
\delta_{ij}s(x) $, they showed that this condition can
be relaxed to $ | \sigma (x) - \sigma (y)| < |x - y|
\log (1 / |x - y|) $, leaving open the question whether
this is true for general $ 2 \times m $ matrices. We
construct a $ 2 \times 1 $ matrix-valued function which
negatively answers this question. The construction
demonstrates an unexpected effect, namely, that
fluctuations in the radial direction may stabilize a
particle in the origin.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stochastic differential equation, pathwise uniqueness
/ strong uniqueness, diffusion process.",
}
@Article{Hambly:2001:PTS,
author = "B. Hambly and James Martin and Neil O'Connell",
title = "{Pitman}'s {$ 2 M - X $} Theorem for Skip-Free Random
Walks with {Markovian} Increments",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "6",
pages = "7:73--7:77",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v6-1036",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1036",
abstract = "Let $ (\xi_k, k \ge 0) $ be a Markov chain on $ {-1, +
1} $ with $ \xi_0 = 1 $ and transition probabilities $
P(\xi_{k + 1} = 1 | \xi_k = 1) = a > b = P(\xi_{k + 1}
= - 1 | \xi_k = - 1) $. Set $ X_0 = 0 $, $ X_n = \xi_1
+ \cdots + \xi_n $ and $ M_n = \max_{0 \le k \le n}X_k
$. We prove that the process $ 2 M - X $ has the same
law as that of $X$ conditioned to stay non-negative.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Pitman's representation, three-dimensional Bessel
process, telegrapher's equation, queue, Burke's
theorem, quasireversibility.",
}
@Article{Bandyopadhyay:2001:HCF,
author = "Antar Bandyopadhyay and David Aldous",
title = "How to Combine Fast Heuristic {Markov} Chain {Monte
Carlo} with Slow Exact Sampling",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "6",
pages = "8:79--8:89",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v6-1037",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1037",
abstract = "Given a probability law $ \pi $ on a set $S$ and a
function $ g : S \rightarrow R$, suppose one wants to
estimate the mean $ \bar {g} = \int g d \pi $. The
Markov Chain Monte Carlo method consists of inventing
and simulating a Markov chain with stationary
distribution $ \pi $. Typically one has no a priori
bounds on the chain's mixing time, so even if
simulations suggest rapid mixing one cannot infer
rigorous confidence intervals for $ \bar {g}$. But
suppose there is also a separate method which (slowly)
gives samples exactly from $ \pi $. Using $n$ exact
samples, one could immediately get a confidence
interval of length $ O(n^{-1 / 2})$. But one can do
better. Use each exact sample as the initial state of a
Markov chain, and run each of these $n$ chains for $m$
steps. We show how to construct confidence intervals
which are always valid, and which, if the (unknown)
relaxation time of the chain is sufficiently small
relative to $ m / n$, have length $ O(n^{-1} \log n)$
with high probability.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Confidence interval, Exact sampling, Markov chain
Monte Carlo.",
}
@Article{Borovkov:2001:KIF,
author = "Konstantin Borovkov and Zaeem Burq",
title = "{Kendall}'s identity for the first crossing time
revisited",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "6",
pages = "9:91--9:94",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v6-1038",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1038",
abstract = "We give a new relatively compact proof of the famous
identity for the distribution of the first hitting time
of a linear boundary by a skip-free process with
stationary independent increments. The proof uses
martingale identities and change of measure.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Skip-free L{\'e}vy process, first crossing time,
change of measure.",
}
@Article{Bertoin:2001:SSS,
author = "Jean Bertoin and Marc Yor",
title = "On Subordinators, Self-Similar {Markov} Processes and
Some Factorizations of the Exponential Variable",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "6",
pages = "10:95--10:106",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v6-1039",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1039",
abstract = "Let $ \xi $ be a subordinator with Laplace exponent $
\Phi $, $ I = \int_0^{\infty } \exp ( - \xi_s)d s $ the
so-called exponential functional, and $X$
(respectively, $ \hat X$) the self-similar Markov
process obtained from $ \xi $ (respectively, from $
\hat {\xi } = - \xi $) by Lamperti's transformation. We
establish the existence of a unique probability measure
$ \rho $ on $]0, \infty [$ with $k$-th moment given for
every $ k \in N$ by the product $ \Phi (1) \cdots \Phi
(k)$, and which bears some remarkable connections with
the preceding variables. In particular we show that if
$R$ is an independent random variable with law $ \rho $
then $ I R$ is a standard exponential variable, that
the function $ t \to E(1 / X_t)$ coincides with the
Laplace transform of $ \rho $, and that $ \rho $ is the
$1$-invariant distribution of the sub-Markovian process
$ \hat X$. A number of known factorizations of an
exponential variable are shown to be of the preceding
form $ I R$ for various subordinators $ \xi $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Self-similar Markov process, subordinator, exponential
functional",
}
@Article{Konig:2001:ELP,
author = "Wolfgang K{\"o}nig and Neil O'Connell",
title = "Eigenvalues of the {Laguerre} Process as Non-Colliding
Squared {Bessel} Processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "6",
pages = "11:107--11:114",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v6-1040",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1040",
abstract = "Let $ A(t) $ be an $ n \times p $ matrix with
independent standard complex Brownian entries and set $
M(t) = A(t)^*A(t) $. This is a process version of the
Laguerre ensemble and as such we shall refer to it as
the {\em Laguerre process\/}. The purpose of this note
is to remark that, assuming $ n > p $, the eigenvalues
of $ M(t) $ evolve like $p$ independent squared Bessel
processes of dimension $ 2 (n - p + 1)$, conditioned
(in the sense of Doob) never to collide. More
precisely, the function $ h(x) = \prod_{i < j}(x_i -
x_j)$ is harmonic with respect to $p$ independent
squared Bessel processes of dimension $ 2 (n - p + 1)$,
and the eigenvalue process has the same law as the
corresponding Doob $h$-transform. In the case where the
entries of $ A(t)$ are {\em real\/} Brownian motions, $
(M(t))_{t > 0}$ is the Wishart process considered by
Bru (1991). There it is shown that the eigenvalues of $
M(t)$ evolve according to a certain diffusion process,
the generator of which is given explicitly. An
interpretation in terms of non-colliding processes does
not seem to be possible in this case. We also identify
a class of processes (including Brownian motion,
squared Bessel processes and generalised
Ornstein--Uhlenbeck processes) which are all amenable
to the same $h$-transform, and compute the
corresponding transition densities and upper tail
asymptotics for the first collision time.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Wishart and Laguerre ensembles and processes,
eigenvalues as diffusions, non-colliding squared Bessel
processes.",
}
@Article{Schramm:2001:PF,
author = "Oded Schramm",
title = "A Percolation Formula",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "6",
pages = "12:115--12:120",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v6-1041",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1041",
abstract = "Let $A$ be an arc on the boundary of the unit disk
$U$. We prove an asymptotic formula for the probability
that there is a percolation cluster $K$ for critical
site percolation on the triangular grid in $U$ which
intersects $A$ and such that $0$ is surrounded by the
union of $K$ and $A$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "SLE, Cardy, conformal invariance",
}
@Article{OConnell:2001:RNC,
author = "Neil O'Connell and Marc Yor",
title = "A Representation for Non-Colliding Random Walks",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "1:1--1:12",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1042",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1042",
abstract = "We define a sequence of mappings $ \Gamma_k : D_0
(R_+)^k \to D_0 (R_+)^k $ and prove the following
result: Let $ N_1, \ldots, N_n $ be the counting
functions of independent Poisson processes on $ R_+ $
with respective intensities $ \mu_1 < \mu_2 < \cdots <
\mu_n $. The conditional law of $ N_1, \ldots, N_n $,
given that\par
$$ N_1 (t) \le \cdots \le N_n(t), \mbox { for all }t
\ge 0, $$
is the same as the unconditional law of $ \Gamma_n(N)
$. From this, we deduce the corresponding results for
independent Poisson processes of equal rates and for
independent Brownian motions (in both of these cases
the conditioning is in the sense of Doob). This extends
a recent observation, independently due to Baryshnikov
(2001) and Gravner, Tracy and Widom (2001), which
relates the law of a certain functional of Brownian
motion to that of the largest eigenvalue of a GUE
random matrix. Our main result can also be regarded as
a generalisation of Pitman's representation for the
3-dimensional Bessel process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "GUE, eigenvalues of random matrices, Hermitian
Brownian motion, non-colliding Brownian motions, Weyl
chamber, queues in series, Burke's theorem,
reversibility, Pitman's representation theorem,
Charlier ensemble.",
}
@Article{Alili:2001:CDC,
author = "Larbi Alili",
title = "Canonical Decompositions of Certain Generalized
{Brownian} Bridges",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "3:27--3:35",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1044",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1044",
abstract = "We define a generalized Brownian bridge and we provide
some information about its filtration. Two
decompositions of this process as a semi-martingale are
given. The first one is a Volterra decomposition and
the second one is its canonical decomposition in its
own filtration.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian bridge; Brownian motion; Canonical
decomposition; Volterra transform.",
}
@Article{Ressel:2001:SAU,
author = "Paul Ressel",
title = "Subdiagonal and Almost Uniform Distributions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "10:97--10:100",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1051",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1051",
abstract = "A distribution (function) $F$ on $ [0, 1]$ with $
F(t)$ less or equal $t$ for all $t$ is called {\em
subdiagonal\/}. The extreme subdiagonal distributions
are identified as those whose distribution functions
are almost surely the identity, or equivalently for
which $ F \circ F = F$. There exists a close connection
to exchangeable random orders on $ \{ 1, 2, 3, \ldots
{} \} $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Subdiagonal distribution, almost uniform distribution,
exchangeable random order.",
}
@Article{Feng:2002:LDQ,
author = "Shui Feng and Jie Xiong",
title = "Large Deviations and Quasi-Potential of a
{Fleming--Viot} Process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "2:13--2:25",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1043",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1043",
abstract = "The large deviation principle is established for the
Fleming--Viot process with neutral mutation when the
process starts from a point on the boundary. Since the
diffusion coefficient is degenerate on the boundary,
the boundary behavior of the process is investigated in
detail. This leads to the explicit identification of
the rate function, the quasi-potential, and the
structure of the effective domain of the rate
function.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Fleming--Viot process, large deviations,
quasi-potential.",
}
@Article{Baudoin:2002:FEG,
author = "Fabrice Baudoin",
title = "Further Exponential Generalization of {Pitman}'s {$ 2
M - X $} Theorem",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "4:37--4:46",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1045",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1045",
abstract = "We present a class of processes which enjoy an
exponential analogue of Pitman's $ 2 M - X $ theorem,
improving hence some works of H. Matsumoto and M.
Yor.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Diffusion processes, Exponential analogue of Pitman's
2M-X theorem.",
}
@Article{Rempala:2002:APS,
author = "Grzegorz Rempala and Jacek Wesolowski",
title = "Asymptotics for Products of Sums and
{$U$}-statistics",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "5:47--5:54",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1046",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1046",
abstract = "The product of subsequent partial sums of independent,
identically distributed, square integrable, positive
random variables is asymptotically lognormal. The
result extends in a rather routine way to
non-degenerate $U$-statistics.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Central limit theorem, lognormal distribution,
products of sums of iid rv's, records, $U$-statistics",
}
@Article{Panchenko:2002:SEI,
author = "Dmitriy Panchenko",
title = "Some Extensions of an Inequality of {Vapnik} and
{Chervonenkis}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "6:55--6:65",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1047",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1047",
abstract = "The inequality of Vapnik and Chervonenkis controls the
expectation of the function by its sample\par
average uniformly over a VC-major class of functions
taking into account the size of the
expectation.\par
Using Talagrand's kernel method we prove a similar
result for the classes of functions for which
Dudley's\par
uniform entropy integral or bracketing entropy integral
is finite.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Concentration of measure, empirical processes",
}
@Article{Haggstrom:2002:MRH,
author = "Olle H{\"a}ggstr{\"o}m",
title = "A Monotonicity Result for Hard-core and
{Widom--Rowlinson} Models on Certain $d$-dimensional
Lattices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "7:67--7:78",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1048",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1048",
abstract = "For each $ d \geq 2 $, we give examples of
$d$-dimensional periodic lattices on which the
hard-core and Widom--Rowlinson models exhibit a phase
transition which is monotonic, in the sense that there
exists a critical value $ \lambda_c$ for the activity
parameter $ \lambda $, such that there is a unique
Gibbs measure (resp. multiple Gibbs measures) whenever
$ \lambda $ is less than $ \lambda_c$ (resp. $ \lambda
$ greater than $ \lambda_c$). This contrasts with
earlier examples of such lattices, where the phase
transition failed to be monotonic. The case of the
cubic lattice $ Z^d$ remains an open problem.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Hard-core model, Widom--Rowlinson model, Gibbs
measures, monotonic phase transition,
site-random-cluster model.",
}
@Article{Klebaner:2002:OPW,
author = "Fima Klebaner",
title = "Option Price When the Stock is a Semimartingale",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "8:79--8:83",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1049",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1049",
abstract = "The purpose of this note is to give a PDE satisfied by
a call option when the price process is a
semimartingale. The main result generalizes the PDE in
the case when the stock price is a diffusion. Its proof
uses Meyer-Tanaka and occupation density formulae.
Presented approach also gives a new insight into the
classical Black-Scholes formula. Rigorous proofs of
some known results are also given.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Black-Scholes formula, Meyer-Tanaka formula,
semimartingales.",
}
@Article{Kessler:2002:IER,
author = "David Kessler and Jeremy Schiff",
title = "{Inclusion-Exclusion} {{\em Redux}}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "9:85--9:96",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1050",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1050",
abstract = "We present a reordered version of the
inclusion--exclusion principle, which is useful when
computing the probability of a union of events which
are close to independent. The advantages of this
formulation are demonstrated in the context of 3
classic problems in combinatorics.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Inclusion-exclusion principle, close-to-independent
events.",
}
@Article{Boivin:2002:GRR,
author = "Daniel Boivin and Jean-Marc Derrien",
title = "Geodesics and Recurrence of Random Walks in Disordered
Systems",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "11:101--11:115",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1052",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1052",
abstract = "In a first-passage percolation model on the square
lattice $ Z^2 $, if the passage times are independent
then the number of geodesics is either $0$ or $ +
\infty $. If the passage times are stationary, ergodic
and have a finite moment of order $ \alpha > 1 / 2$,
then the number of geodesics is either $0$ or $ +
\infty $. We construct a model with stationary passage
times such that $ E \lbrack t(e)^\alpha \rbrack <
\infty $, for every $ 0 < \alpha < 1 / 2$, and with a
unique geodesic. The recurrence/transience properties
of reversible random walks in a random environment with
stationary conductances $ (a(e); e$ is an edge of $
\mathbb {Z}^2)$ are considered.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Geodesics in first-passage percolation model; Random
environment with stationary conductances; Recurrence
and transience.; Reversible random walks on $Z^2$",
}
@Article{Soucaliuc:2002:NRB,
author = "Florin Soucaliuc and Wendelin Werner",
title = "A Note on Reflecting {Brownian} Motions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "12:117--12:122",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1053",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1053",
abstract = "We give another proof of the following result from a
joint paper with B{\'a}lint T{\'o}th: {\em A Brownian
motion reflected on an independent time-reversed
Brownian motion is a Brownian motion.}",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion, reflection",
}
@Article{Rosenthal:2002:QCR,
author = "Jeffrey Rosenthal",
title = "Quantitative Convergence Rates of {Markov} Chains: A
Simple Account",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "13:123--13:128",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1054",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1054",
abstract = "We state and prove a simple quantitative bound on the
total variation distance after $k$ iterations between
two Markov chains with different initial distributions
but identical transition probabilities. The result is a
simplified and improved version of the result in
Rosenthal (1995), which also takes into account the $
\epsilon $-improvement of Roberts and Tweedie (1999),
and which follows as a special case of the more
complicated time-inhomogeneous results of Douc et al.
(2002). However, the proof we present is very short and
simple; and we feel that it is worthwhile to boil the
proof down to its essence. This paper is purely
expository; no new results are presented.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Markov chain, convergence rate, mixing time, drift
condition, minorisation condition, total variation
distance.",
}
@Article{Atar:2002:NLN,
author = "Rami Atar and Krzysztof Burdzy",
title = "On Nodal Lines of {Neumann} Eigenfunctions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "14:129--14:139",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1055",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1055",
abstract = "We present a new method for locating the nodal line of
the second eigenfunction for the Neumann problem in a
planar domain.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Nodal line, reflected Brownian motion, mirror
coupling, eigenfunction, Neumann problem",
}
@Article{Machida:2002:FAA,
author = "Motoya Machida",
title = "{Fill}'s Algorithm for Absolutely Continuous
Stochastically Monotone Kernels",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "15:141--15:155",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1056",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1056",
abstract = "Fill, Machida, Murdoch, and Rosenthal (2000) presented
their algorithm and its variants to extend the perfect
sampling algorithm of Fill (1998) to chains on
continuous state spaces. We consider their algorithm
for absolutely continuous stochastically monotone
kernels, and show the correctness of the algorithm
under a set of certain regularity conditions. These
conditions succeed in relaxing the previously known
hypotheses sufficient for their algorithm to apply.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Markov chain Monte Carlo, Fill's algorithm, perfect
sampling, exact sampling, rejection sampling,
stochastic monotonicity, partially ordered set,
monotone coupling, absolutely continuous Markov kernel,
regularity conditions.",
}
@Article{Wang:2002:SCC,
author = "Hao Wang",
title = "State Classification for a Class of Interacting
Superprocesses with Location Dependent Branching",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "16:157--16:167",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1057",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1057",
abstract = "The spatial structure of a class of superprocesses
which arise as limits in distribution of a class of
interacting particle systems with location dependent
branching is investigated. The criterion of their state
classification is obtained. Their effective state space
is contained in the set of purely-atomic measures or
the set of absolutely continuous measures according as
one diffusive coefficient $ c(x) \equiv 0 $ or $ |c(x)|
\geq \epsilon > 0 $ while another diffusive coefficient
$ h \in C^2_b(R) $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "spatial structure, interaction, superprocess, location
dependent branching",
}
@Article{Bahlali:2002:EUS,
author = "Khaled Bahlali",
title = "Existence and uniqueness of solutions for {BSDEs} with
locally {Lipschitz} coefficient",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "17:169--17:179",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1058",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1058",
abstract = "We deal with multidimensional backward stochastic
differential equations (BSDE) with locally Lipschitz
coefficient in both variables $ y, z $ and an only
square integrable terminal data. Let $ L_N $ be the
Lipschitz constant of the coefficient on the ball $
B(0, N) $ of $ R^d \times R^{dr} $. We prove that if $
L_N = O (\sqrt {\log N }) $, then the corresponding
BSDE has a unique solution. Moreover, the stability of
the solution is established under the same assumptions.
In the case where the terminal data is bounded, we
establish the existence and uniqueness of the solution
also when the coefficient has an arbitrary growth (in
$y$) and without restriction on the behaviour of the
Lipschitz constant $ L_N $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Backward stochastic differential equations (BSDE),
locally Lipschitz function.",
}
@Article{Griffin:2002:TSS,
author = "Philip Griffin",
title = "Tightness of the {Student} $t$-Statistic",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "18:181--18:190",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1059",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1059",
abstract = "Let $ X, X_1, X_2, \dots $ be a sequence of
nondegenerate, independent and identically distributed
random variables and set $ S_n = X_1 + \dots + X_n $, $
V_n^2 = X_1^2 + \dots + X_n^2 $. We answer a question
of Gotze, Gine and Mason by providing a simple
necessary and sufficient condition for tightness of $
S_n / V_n $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "tightness, t-statistic, self-normalized sum",
}
@Article{Zerner:2002:NBL,
author = "Martin Zerner",
title = "A Non-Ballistic Law of Large Numbers for Random Walks
in {I.I.D.} Random Environment",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "19:191--19:197",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1060",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1060",
abstract = "We prove that random walks in i.i.d. random
environments which oscillate in a given direction have
velocity zero with respect to that direction. This
complements existing results thus giving a general law
of large numbers under the only assumption of a certain
zero-one law, which is known to hold if the dimension
is two.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random walk in random environment, RWRE, law of large
numbers.",
}
@Article{Mikami:2002:OCA,
author = "Toshio Mikami",
title = "Optimal Control for Absolutely Continuous Stochastic
Processes and the Mass Transportation Problem",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "20:199--20:213",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1061",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1061",
abstract = "We study the optimal control problem for $ \mathbb
{R}^d$-valued absolutely continuous stochastic
processes with given marginal distributions at every
time. When $ d = 1$, we show the existence and the
uniqueness of a minimizer which is a function of a time
and an initial point. When $ d > 1$, we show that a
minimizer exists and that minimizers satisfy the same
ordinary differential equation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Absolutely continuous stochastic process, mass
transportation problem, Salisbury's problem, Markov
control, zero-noise limit",
}
@Article{vanZanten:2002:COM,
author = "Harry van Zanten",
title = "Continuous {Ocone} Martingales as Weak Limits of
Rescaled Martingales",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "21:215--21:222",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1062",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See remark and counterexample
\cite{Peccati:2004:WCO}.",
URL = "http://ecp.ejpecp.org/article/view/1062",
abstract = "Consider a martingale $M$ with bounded jumps and two
sequences $ a_n, b_n \to \infty $. We show that if the
rescaled martingales\par
$$ M^n_t = \frac {1}{\sqrt {a_n}}M_{b_n t} $$
converge weakly, then the limit is necessarily a
continuous Ocone martingale. Necessary and sufficient
conditions for the weak convergence of the rescaled
martingales are also given.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Appleby:2002:ASS,
author = "John Appleby",
title = "Almost Sure Stability of Linear {It{\^o}--Volterra}
Equations with Damped Stochastic Perturbations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "7",
pages = "22:223--22:234",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v7-1063",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1063",
abstract = "In this paper we study the a.s. convergence of all
solutions of the It{\^o}--Volterra equation
$$ d X(t) = (A X(t) + \int_0^t K(t - s)X(s), d s) \, d
t + \Sigma (t) \, d W(t) $$
to zero. $A$ is a constant $ d \times d$ matrix, $K$ is
a $ d \times d$ continuous and integrable matrix
function, $ \Sigma $ is a continuous $ d \times r$
matrix function, and $W$ is an $r$-dimensional Brownian
motion. We show that when
$$ x'(t) = A x(t) + \int_0^t K(t - s)x(s) \, d s $$
has a uniformly asymptotically stable zero solution,
and the resolvent has a polynomial upper bound, then
$X$ converges to 0 with probability 1, provided
$$ \lim_{t \rightarrow \infty } | \Sigma (t)|^2 \log t
= 0. $$
A converse result under a monotonicity restriction on $
| \Sigma |$ establishes that the rate of decay for $ |
\Sigma |$ above is necessary. Equations with bounded
delay and neutral equations are also considered.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stochastic functional-differential equations,
It{\^o}--Volterra equations, uniform asymptotic
stability, almost sure stability, pathwise stability,
simulated annealing.",
}
@Article{Gao:2003:MML,
author = "Fuchang Gao",
title = "The Mean of a Maximum Likelihood Estimator Associated
with the {Brownian} Bridge",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "1:1--1:5",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1064",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1064",
abstract = "A closed formula for the mean of a maximum likelihood
estimator associated with the Brownian bridge is
obtained; the exact relation with that of the Brownian
motion is established.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian bridge, intrinsic volume, solid angle",
}
@Article{Angel:2003:RWA,
author = "Omer Angel and Itai Benjamini and B{\'a}lint
Vir{\'a}g",
title = "Random Walks that Avoid Their Past Convex Hull",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "2:6--2:16",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1065",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1065",
abstract = "We explore planar random walk conditioned to avoid its
past convex hull. We prove that it escapes at a
positive lim sup speed. Experimental results show that
fluctuations from a limiting direction are on the order
of $ n^{3 / 4} $. This behavior is also observed for
the extremal investor, a natural financial model
related to the planar walk.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Holroyd:2003:TMP,
author = "Alexander Holroyd and Yuval Peres",
title = "Trees and Matchings from Point Processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "3:17--3:27",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1066",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1066",
abstract = "A {\em factor graph\/} of a point process is a graph
whose vertices are the points of the process, and which
is constructed from the process in a deterministic
isometry-invariant way. We prove that the {\em
d\/}-dimensional Poisson process has a one-ended tree
as a factor graph. This implies that the Poisson points
can be given an ordering isomorphic to the usual
ordering of the integers in a deterministic
isometry-invariant way. For $d$ greater than or equal
to 4 our result answers a question posed by Ferrari,
Landim and Thorisson [7]. We prove also that any
isometry-invariant ergodic point process of finite
intensity in Euclidean or hyperbolic space has a
perfect matching as a factor graph provided all the
inter-point distances are distinct.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Poisson process, point process, random tree, random
matching, minimal spanning forest.",
}
@Article{Dubedat:2003:ST,
author = "Julien Dub{\'e}dat",
title = "{SLE} and Triangles",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "4:28--4:42",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1067",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1067",
abstract = "By analogy with Carleson's observation on Cardy's
formula describing crossing probabilities for the
scaling limit of critical percolation, we exhibit
``privileged geometries'' for Stochastic Loewner
Evolutions with various parameters, for which certain
hitting distributions are uniformly distributed. We
then examine consequences for limiting probabilities of
events concerning various critical plane discrete
models.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stochastic Loewner Evolution. FK percolation. Double
domino tilings. Uniform spanning tree.",
}
@Article{Duheille-Bienvenue:2003:CLT,
author = "Fr{\'e}d{\'e}rique Duheille-Bienvenue and Nadine
Guillotin-Plantard",
title = "{Central Limit Theorems} for the Products of Random
Matrices Sampled by a Random Walk",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "5:43--5:50",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1068",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1068",
abstract = "The purpose of the present paper is to study the
asymptotic behaviour of the products of random matrices
indexed by a random walk following the results obtained
by Furstenberg and Kesten (MR53:14670) and by Ishitani
(MR 53:14670).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random Walk, Random Matrix, Random Scenery, Functional
limit theorem",
}
@Article{Gobet:2003:CGB,
author = "Emmanuel Gobet and Arturo Kohatsu-Higa",
title = "Computation of {Greeks} for Barrier and Lookback
Options Using {Malliavin} Calculus",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "6:51--6:62",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1069",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1069",
abstract = "In this article, we consider the numerical
computations associated to the Greeks of barrier and
lookback options, using Malliavin calculus. For this,
we derive some integration by parts formulae involving
the maximum and minimum of a one dimensional diffusion.
Numerical tests illustrate the gain of accuracy
compared to classical methods.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Barrier and lookback options. Option sensitivities.
Malliavin calculus.",
}
@Article{Sepanski:2003:LIL,
author = "Steven Sepanski",
title = "A Law of the Iterated Logarithm for the Sample
Covariance Matrix",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "7:63--7:76",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1070",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1070",
abstract = "For a sequence of independent identically distributed
Euclidean random vectors, we prove a law of the
iterated logarithm for the sample covariance matrix
when {\em o(log log n) \/}terms are omitted. The result
is proved under the hypothesis that the random vectors
belong to the generalized domain of attraction of the
multivariate Gaussian law. As an application, we obtain
a bounded law of the iterated logarithm for the
multivariate t-statistic.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "law of the iterated logarithm, sample covariance,
central limit theorem, generalized domain of
attraction, multivariate t statistic, extreme values,
operator normalization, self normalization",
}
@Article{Wilson:2003:MTR,
author = "David Wilson",
title = "Mixing Time of the {Rudvalis} Shuffle",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "8:77--8:85",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1071",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1071",
abstract = "We extend a technique for lower-bounding the mixing
time of card-shuffling Markov chains, and use it to
bound the mixing time of the Rudvalis Markov chain, as
well as two variants considered by Diaconis and
Saloff-Coste. We show that in each case $ \Theta (n^3
\log n) $ shuffles are required for the permutation to
randomize, which matches (up to constants) previously
known upper bounds. In contrast, for the two variants,
the mixing time of an individual card is only $ \Theta
(n^2) $ shuffles.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Markov chain, card shuffling, mixing time",
}
@Article{Benjamini:2003:ERW,
author = "Itai Benjamini and David Wilson",
title = "Excited Random Walk",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "9:86--9:92",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1072",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1072",
abstract = "A random walk on $ \mathbb {Z}^d $ is excited if the
first time it visits a vertex there is a bias in one
direction, but on subsequent visits to that vertex the
walker picks a neighbor uniformly at random. We show
that excited random walk on $ \mathbb {Z}^d $ is
transient iff $ d > 1 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Perturbed random walk, transience",
}
@Article{Tracy:2003:SDE,
author = "Craig Tracy and Harold Widom",
title = "A System of Differential Equations for the {Airy}
Process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "10:93--10:98",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1074",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1074",
abstract = "The Airy process is characterized by its
$m$-dimensional distribution functions. For $ m = 1$ it
is known that this distribution function is expressible
in terms of a solution to Painleve II. We show that
each finite-dimensional distribution function is
expressible in terms of a solution to a system of
differential equations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Airy process. Extended Airy kernel. Growth processes.
Integrable differential equations.",
}
@Article{Weininger:2003:PCI,
author = "Nicholas Weininger",
title = "Positive correlation for increasing events with
disjoint dependencies does not imply positive
correlation for all increasing events",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "11:99--11:101",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1078",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1078",
abstract = "A probability measure $ \mu $ on the lattice $ 2^{[n]}
$ is said to be positively associated if any two
increasing functions on the lattice are positively
correlated with respect to $ \mu $. Pemantle asked
whether, in order to establish positive association for
a given mu, it might be sufficient to show positive
correlation only for pairs of functions which depend on
disjoint subsets of the ground set $ [n] $. We answer
Pemantle's question in the negative, by exhibiting a
measure which gives positive correlation for pairs
satisfying Pemantle's condition but not for general
pairs of increasing functions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Zaidi:2003:SLS,
author = "Noureddine Za{\"\i}di and David Nualart",
title = "Smoothness of the law of the supremum of the
fractional {Brownian} motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "12:102--12:111",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1079",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1079",
abstract = "This note is devoted to prove that the supremum of a
fractional Brownian motion with Hurst parameter $ H \in
\left (0, 1 \right) $ has an infinitely differentiable
density on $ \left (0, \infty \right) $. The proof of
this result is based on the techniques of the Malliavin
calculus.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Malliavin calculus, fractional Brownian motion,
fractional calculus",
}
@Article{Katori:2003:NBM,
author = "Makoto Katori and Hideki Tanemura",
title = "Noncolliding {Brownian} motions and {Harish-Chandra}
formula",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "13:112--13:121",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1076",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1076",
abstract = "We consider a system of noncolliding Brownian motions
introduced in our previous paper, in which the
noncolliding condition is imposed in a finite time
interval $ (0, T] $. This is a temporally inhomogeneous
diffusion process whose transition probability density
depends on a value of $T$, and in the limit $ T \to
\infty $ it converges to a temporally homogeneous
diffusion process called Dyson's model of Brownian
motions. It is known that the distribution of particle
positions in Dyson's model coincides with that of
eigenvalues of a Hermitian matrix-valued process, whose
entries are independent Brownian motions. In the
present paper we construct such a Hermitian
matrix-valued process, whose entries are sums of
Brownian motions and Brownian bridges given
independently of each other, that its eigenvalues are
identically distributed with the particle positions of
our temporally inhomogeneous system of noncolliding
Brownian motions. As a corollary of this identification
we derive the Harish-Chandra formula for an integral
over the unitary group.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "random matrices, Dyson's Brownian motion, Imhof's
relation, Harish-Chandra formula.",
}
@Article{Boufoussi:2003:SDF,
author = "Brahim Boufoussi and Youssef Ouknine",
title = "On a {SDE} driven by a fractional {Brownian} motion
and with monotone drift",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "14:122--14:134",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1084",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1084",
abstract = "Let $ {B_t^H, t \in \lbrack 0, T]} $ be a fractional
Brownian motion with Hurst parameter $ H > \frac {1}{2}
$. We prove the existence of a weak solution for a
stochastic differential equation of the form $ X_t = x
+ B_t^H + \int_0^t \left (b_1 (s, X_s) + b_2 (s, X_s)
\right) d s $, where $ b_1 (s, x) $ is a Holder
continuous function of order strictly larger than $ 1 -
\frac {1}{2H} $ in $x$ and than $ H - \frac {1}{2}$ in
time and $ b_2$ is a real bounded nondecreasing and
left (or right) continuous function.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Fractional Brownian motion, Stochastic integrals,
Girsanov transform",
}
@Article{Lalley:2003:SCL,
author = "Steven Lalley",
title = "Strict Convexity of the Limit Shape in First-Passage
Percolation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "15:135--15:141",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1089",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1089",
abstract = "Sufficient conditions are given for the strict
convexity of the limit shape in standard first-passage
percolation. These conditions involve (1) asymptotic
``straightness'' of the geodesics, and (2) existence of
mean-zero limit distributions for the first-passage
times.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Revelle:2003:HKA,
author = "David Revelle",
title = "Heat Kernel Asymptotics on the Lamplighter Group",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "16:142--16:154",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1092",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1092",
abstract = "We show that, for one generating set, the on-diagonal
decay of the heat kernel on the lamplighter group is
asymptotic to $ c_1 n^{1 / 6} \exp [ - c_2 n^{1 / 3}]
$. We also make off-diagonal estimates which show that
there is a sharp threshold for which elements have
transition probabilities that are comparable to the
return probability. The off-diagonal estimates also
give an upper bound for the heat kernel that is
uniformly summable in time. The methods used also apply
to a one dimensional trapping problem, and we compute
the distribution of the walk conditioned on survival as
well as a corrected asymptotic for the survival
probability. Conditioned on survival, the position of
the walker is shown to be concentrated within $ \alpha
n^{1 / 3} $ of the origin for a suitable $ \alpha $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Bertoin:2003:PTF,
author = "Jean Bertoin and Loic Chaumont and Jim Pitman",
title = "Path transformations of first passage bridges",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "17:155--17:166",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1096",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1096",
abstract = "We define the first passage bridge from 0 to $ \lambda
$ as the Brownian motion on the time interval $ [0, 1]
$ conditioned to first hit $ \lambda $ at time 1. We
show that this process may be related to the Brownian
bridge, the Bessel bridge or the Brownian excursion via
some path transformations, the main one being an
extension of Vervaat's transformation. We also propose
an extension of these results to certain bridges with
cyclically exchangeable increments.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Lugosi:2003:NRC,
author = "G{\'a}bor Lugosi and Shahar Mendelson and Vladimir
Koltchinskii",
title = "A note on the richness of convex hulls of {VC}
classes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "18:167--18:169",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1097",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1097",
abstract = "We prove the existence of a class $A$ of subsets of $
\mathbb {R}^d$ of VC dimension 1 such that the
symmetric convex hull $F$ of the class of
characteristic functions of sets in $A$ is rich in the
following sense. For any absolutely continuous
probability measure $ \mu $ on $ \mathbb {R}^d$,
measurable set $B$ and $ \varepsilon > 0$, there exists
a function $f$ in $F$ such that the measure of the
symmetric difference of $B$ and the set where $f$ is
positive is less than $ \varepsilon $. The question was
motivated by the investigation of the theoretical
properties of certain algorithms in machine learning.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Guiol:2003:MSD,
author = "Herve Guiol and Krishnamurthi Ravishankar and Ellen
Saada",
title = "Microscopic structure of a decreasing shock for the
asymmetric $k$-step exclusion process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "19:170--19:178",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1080",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1080",
abstract = "The asymmetric $k$-step exclusion processes are the
simplest interacting particle systems whose
hydrodynamic equation may exhibit both increasing and
decreasing entropic shocks under Euler scaling. We
prove that, under Riemann initial condition with right
density zero and adequate left density, the rightmost
particle identifies microscopically the decreasing
shock.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Asymmetric k-step exclusion process, Non-convex or
non-concave flux, microscopic shock, rightmost
particle",
}
@Article{Kovchegov:2003:LSL,
author = "Yevgeniy Kovchegov and Scott Sheffield",
title = "Linear Speed Large Deviations for Percolation
Clusters",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "20:179--20:183",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1098",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1098",
abstract = "Let $ C_n $ be the origin-containing cluster in
subcritical percolation on the lattice $ \frac {1}{n}
\mathbb Z^d $, viewed as a random variable in the space
$ \Omega $ of compact, connected, origin-containing
subsets of $ \mathbb R^d $, endowed with the Hausdorff
metric $ \delta $. When $ d \geq 2 $, and $ \Gamma $ is
any open subset of $ \Omega $, we prove that\par
$$ \lim_{n \rightarrow \infty } \frac {1}{n} \log
P(C_n \in \Gamma) = - \inf_{S \in \Gamma } \lambda (S)
$$
where $ \lambda (S) $ is the one-dimensional Hausdorff
measure of $S$ defined using the {\em correlation
norm\/}:\par
$$ ||u|| := \lim_{n \rightarrow \infty } - \frac
{1}{n} \log P (u_n \in C_n) $$
where $ u_n$ is $u$ rounded to the nearest element of $
\frac {1}{n} \mathbb Z^d$. Given points $ a^1, \ldots,
a^k \in \mathbb R^d$, there are finitely many
correlation-norm Steiner trees spanning these points
and the origin. We show that if the $ C_n$ are each
conditioned to contain the points $ a^1_n, \ldots,
a^k_n$, then the probability that $ C_n$ fails to
approximate one of these trees tends to zero
exponentially in $n$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Kahn:2003:ITC,
author = "Jeff Kahn",
title = "Inequality of Two Critical Probabilities for
Percolation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "8",
pages = "21:184--21:187",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v8-1099",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1099",
abstract = "We disprove a conjecture of Russ Lyons---that for
every locally finite, connected graph $G$, the critical
probability for (Bernoulli bond) percolation on $G$ is
equal to the {"first} moment {method"} lower bound on
this probability---and propose a possible
alternative.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Londono:2004:STN,
author = "Jaime Londono",
title = "State Tameness: A New Approach for Credit Constrains",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "1:1--1:13",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1102",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1102",
abstract = "We propose a new definition for tameness within the
model of security prices as It{\^o} processes that is
risk-aware. We give a new definition for arbitrage and
characterize it. We then prove a theorem that can be
seen as an extension of the second fundamental theorem
of asset pricing, and a theorem for valuation of
contingent claims of the American type. The valuation
of European contingent claims and American contingent
claims that we obtain does not require the full range
of the volatility matrix. The technique used to prove
the theorem on valuation of American contingent claims
does not depend on the Doob-Meyer decomposition of
super-martingales; its proof is constructive and
suggest and alternative way to find approximations of
stopping times that are close to optimal.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Csaki:2004:IPR,
author = "Endre Csaki and Yueyun Hu",
title = "Invariance Principles for Ranked Excursion Lengths and
Heights",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "2:14--2:21",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1103",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1103",
abstract = "In this note we prove strong invariance principles
between ranked excursion lengths and heights of a
simple random walk and those of a standard Brownian
motion. Some consequences concerning limiting
distributions and strong limit theorems will also be
presented.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Birkner:2004:CWD,
author = "Matthias Birkner",
title = "A Condition for Weak Disorder for Directed Polymers in
Random Environment",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "3:22--3:25",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1104",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1104",
abstract = "We give a sufficient criterion for the weak disorder
regime of directed polymers in random environment,
which extends a well-known second moment criterion. We
use a stochastic representation of the size-biased law
of the partition function.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Hara:2004:FDD,
author = "Keisuke Hara",
title = "Finite dimensional determinants as characteristic
functions of quadratic {Wiener} functionals",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "4:26--4:35",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1091",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1091",
abstract = "We show a method and the structure to calculate the
characteristic functions of quadratic Wiener
functionals by using classical Weierstrass-Hadamard's
theory on entire functions. We also examine the idea by
an example for Gaussian processes with multiple
Markovian property.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "entire functions; generalized determinants; quadratic
Wiener functionals",
}
@Article{Xiong:2004:LTB,
author = "Jie Xiong",
title = "Long-term behavior for superprocesses over a
stochastic flow",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "5:36--5:52",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1081",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1081",
abstract = "We study the limit of a superprocess controlled by a
stochastic flow as $ t \to \infty $. It is proved that
when $ d \le 2 $, this process suffers long-time local
extinction; when $ d \ge 3 $, it has a limit which is
persistent. The stochastic log-Laplace equation
conjectured by Skoulakis and Adler (2001) and studied
by this author (2004) plays a key role in the proofs
like the one played by the log-Laplace equation in
deriving long-term behavior for usual super-Brownian
motion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Superprocess, stochastic flow, log-Laplace equation,
long-term behavior.",
}
@Article{Timar:2004:TGF,
author = "Adam Timar",
title = "Tree and Grid factors of General Point processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "6:53--6:59",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1073",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1073",
abstract = "We study isomorphism invariant point processes of $
R^d $ whose groups of symmetries are almost surely
trivial. We define a 1-ended, locally finite tree
factor on the points of the process, that is, a mapping
of the point configuration to a graph on it that is
measurable and equivariant with the point process. This
answers a question of Holroyd and Peres. The tree will
be used to construct a factor isomorphic to $ Z^n $.
This perhaps surprising result (that any $d$ and $n$
works) solves a problem by Steve Evans. The
construction, based on a connected clumping with $ 2^i$
vertices in each clump of the $i$'th partition, can be
used to define various other factors.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "factors; Point Processes; random grid; random tree",
}
@Article{Biggins:2004:LDM,
author = "J. D. Biggins",
title = "Large Deviations for Mixtures",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "7:60--7:71",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1106",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1106",
abstract = "The results discussed here are most easily described
in words using Bayesian terminology. For each $n$,
there are probability distributions for the data
conditional on a parameter, and there is also a prior
distribution for the parameter. Integrating out, using
the prior, gives the (unconditional) distribution for
the data, for each $n$. The question considered here is
when large deviation principles for the conditional
distributions and for the prior distributions imply a
large deviation principle for the unconditional
distributions. Chaganty (1997) also considered this
question, but under stronger assumptions. The treatment
here follows that of Dinwoodie and Zabell (1992) who,
motivated by exchangeability, considered the case where
the prior does not vary with $n$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Krishnapur:2004:RGW,
author = "Manjunath Krishnapur and Yuval Peres",
title = "Recurrent Graphs where Two Independent Random Walks
Collide Finitely Often",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "8:72--8:81",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1111",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1111",
abstract = "We present a class of graphs where simple random walk
is recurrent, yet two independent walkers meet only
finitely many times almost surely. In particular, the
comb lattice, obtained from $ Z^2 $ by removing all
horizontal edges off the $x$-axis, has this property.
We also conjecture that the same property holds for
some other graphs, including the incipient infinite
cluster for critical percolation in $ Z^2$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Soshnikov:2004:PSL,
author = "Alexander Soshnikov",
title = "{Poisson} Statistics for the Largest Eigenvalues of
{Wigner} Random Matrices with Heavy Tails",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "9:82--9:91",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1112",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1112",
abstract = "We study large Wigner random matrices in the case when
the marginal distributions of matrix entries have heavy
tails. We prove that the largest eigenvalues of such
matrices have Poisson",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Burdzy:2004:GO,
author = "Krzysztof Burdzy and David White",
title = "A {Gaussian} Oscillator",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "10:92--10:95",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1113",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1113",
abstract = "We present a stochastic process with sawtooth paths
whose distribution is given by a simple rule and whose
stationary distribution is Gaussian. The process arose
in a natural way in research on interaction of an inert
particle with a Brownian particle.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Song:2004:SBG,
author = "Renming Song and Zoran Vondracek",
title = "Sharp Bounds for {Green} and Jumping Functions of
Subordinate Killed {Brownian} Motions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "11:96--11:105",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1114",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1114",
abstract = "In this paper we obtain sharp bounds for the Green
function and jumping function of a subordinate killed
Brownian motion in a bounded $ C^{1, 1} $ domain, where
the subordinating process is a subordinator whose
Laplace exponent has certain asymptotic behavior at
infinity.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Appleby:2004:ONO,
author = "John Appleby and Conall Kelly",
title = "Oscillation and Non-oscillation in Solutions of
Nonlinear Stochastic Delay Differential Equations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "12:106--12:118",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1115",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1115",
abstract = "This paper studies the oscillation and nonoscillation
of solutions of a nonlinear stochastic delay
differential equation, where the noise perturbation
depends on the current state, and the drift depends on
a delayed argument. When the restoring force towards
equilibrium is relatively strong, all solutions
oscillate, almost surely. However, if the restoring
force is superlinear, positive solutions exist with
positive probability, and for suitably chosen initial
conditions, the probability of positive solutions can
be made arbitrarily close to unity.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Louis:2004:EPE,
author = "Pierre-Yves Louis",
title = "Ergodicity of {PCA}: Equivalence between Spatial and
Temporal Mixing Conditions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "13:119--13:131",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1116",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1116",
abstract = "For a general attractive Probabilistic Cellular
Automata on $ S^{\mathbb {Z}^d} $, we prove that the
(time-) convergence towards equilibrium of this
Markovian parallel dynamics, exponentially fast in the
uniform norm, is equivalent to a condition ($ \mathcal
{A}$). This condition means the exponential decay of
the influence from the boundary for the invariant
measures of the system restricted to finite boxes. For
a class of reversible PCA dynamics on $ \{ - 1; + 1
\}^{\mathbb {Z}^d}$ with a naturally associated
Gibbsian potential $ \varphi $, we prove that a
(spatial-) weak mixing condition ($ \mathcal {WM}$) for
$ \varphi $ implies the validity of the assumption ($
\mathcal {A}$); thus {\em exponential (time-)
ergodicity\/} of these dynamics towards the unique
Gibbs measure associated to $ \varphi $ holds. On some
particular examples we state that exponential
ergodicity holds as soon as there is no phase
transition.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Jonasson:2004:OSR,
author = "Johan Jonasson",
title = "On the optimal strategy in a random game",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "14:132--14:139",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1100",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1100",
abstract = "Consider a two-person zero-sum game played on a random
$n$ by $n$ matrix where the entries are iid normal
random variables. Let $Z$ be the number of rows in the
support of the optimal strategy for player I given the
realization of the matrix. (The optimal strategy is
a.s. unique and $Z$ a.s. coincides with the number of
columns of the support of the optimal strategy for
player II.) Faris an Maier (see the references) make
simulations that suggest that as $n$ gets large $Z$ has
a distribution close to binomial with parameters $n$
and 1/2 and prove that $ P(Z = n) < 2^{-(k - 1)}$. In
this paper a few more theoretically rigorous steps are
taken towards the limiting distribution of $Z$: It is
shown that there exists $ a < 1 / 2$ (indeed $ a <
0.4$) such that $ P((1 / 2 - a)n < Z < (1 / 2 + a)n)$
tends to 1 as $n$ increases. It is also shown that the
expectation of $Z$ is $ (1 / 2 + o(1))n$. We also prove
that the value of the game with probability $ 1 - o(1)$
is at most $ C n^{-1 / 2}$ for some finite $C$
independent of $n$. The proof suggests that an upper
bound is in fact given by $ f(n) / n$, where $ f(n)$ is
any sequence tending to infinity as $n$ increases, and
it is pointed out that if this is true, then the
variance of $Z$ is $ o(n^2)$ so that any $ a > 0$ will
do in the bound on $Z$ above.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "two-person game, mixed strategy, equalizing strategy,
saddle point",
}
@Article{Kendall:2004:GEP,
author = "Wilfrid Kendall",
title = "Geometric Ergodicity and Perfect Simulation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "15:140--15:151",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1117",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1117",
abstract = "This note extends the work of Foss and Tweedie (1998),
who showed that availability of the classic Coupling
from the Past (CFTP) algorithm of Propp and Wilson
(1996) is essentially equivalent to uniform ergodicity
for a Markov chain (see also Hobert and Robert, 2004).
In this note we show that all geometrically ergodic
chains possess dominated CFTP algorithms (not
necessarily practical!) which are rather closely
connected to Foster-Lyapunov criteria. Hence geometric
ergodicity implies dominated CFTP.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Jarai:2004:BDH,
author = "Antal Jarai and Harry Kesten",
title = "A Bound for the Distribution of the Hitting Time of
Arbitrary Sets by Random Walk",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "16:152--16:161",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1119",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1119",
abstract = "We consider a random walk $ S_n = \sum_{i = 1}^n X_i $
with i.i.d. $ X_i $. We assume that the $ X_i $ take
values in $ \mathbb {Z^d} $, have bounded support and
zero mean. For $ A \subset \mathbb {Z^d}, A \ne
\emptyset $ we define $ \tau_A = \inf {n \ge 0 : S_n
\in A} $. We prove that there exists a constant $C$,
depending on the common distribution of the $ X_i$ and
$d$ only, such that $ \sup_{\emptyset \ne A \subset
\mathbb {Z^d}} P \{ \tau_A = n \} \le C / n, n \ge
1$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Gine:2004:SNC,
author = "Evarist Gin{\'e} and Friedrich G{\"o}tze",
title = "On Standard Normal Convergence of the Multivariate
{Student} $t$-Statistic for Symmetric Random Vectors",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "17:162--17:171",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1120",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1120",
abstract = "It is proved that if the multivariate Student
$t$-statistic based on i.i.d. symmetric random vectors
is asymptotically standard normal, then these random
vectors are in the generalized domain of attraction of
the normal law. Uniform integrability is also
considered, even in the absence of symmetry.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Peccati:2004:WCO,
author = "Giovanni Peccati",
title = "Weak Convergence to {Ocone} Martingales: a Remark",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "18:172--18:174",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1121",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See \cite{vanZanten:2002:COM}.",
URL = "http://ecp.ejpecp.org/article/view/1121",
abstract = "We show, by a simple counterexample, that the main
result in a recent paper by H. Van Zanten [Electronic
Communications in Probability {\bf 7} (2002), 215--222]
is false. We eventually point out the origin of the
error.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Friedli:2004:LRP,
author = "Sacha Friedli and Beno{\^\i}te Borge de Lima and
Vladas Sidoravicius",
title = "On Long Range Percolation with Heavy Tails",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "19:175--19:177",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1122",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1122",
abstract = "Consider independent long range percolation on $
\mathbf {Z}^d $, $ d \geq 2 $, where edges of length
$n$ are open with probability $ p_n$. We show that if $
\limsup_{n \to \infty }p_n > 0, $ then there exists an
integer $N$ such that $ P_N(0 \leftrightarrow \infty) >
0$, where $ P_N$ is the truncated measure obtained by
taking $ p_{N, n} = p_n$ for $ n \leq N$ and $ p_{N, n}
= 0$ for all $ n > N$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Janson:2004:CMI,
author = "Svante Janson and Philippe Chassaing",
title = "The Center of Mass of the {ISE} and the {Wiener} Index
of Trees",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "9",
pages = "20:178--20:187",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v9-1088",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1088",
abstract = "We derive the distribution of the center of mass S of
the integrated superBrownian excursion (ISE) from the
asymptotic distribution of the Wiener index for simple
trees. Equivalently, this is the distribution of the
integral of a Brownian snake. A recursion formula for
the moments and asymptotics for moments and tail
probabilities are derived.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian excursion; Brownian snake; center of mass;
ISE; Wiener index",
}
@Article{Morandin:2005:RBP,
author = "Francesco Morandin",
title = "A Resummed Branching Process Representation for a
Class of Nonlinear {ODEs}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "1:1--1:6",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1126",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1126",
abstract = "We study some probabilistic representations, based on
branching processes, of a simple nonlinear differential
equation, i.e. $ u' = \lambda u(a u^R - 1) $. The first
approach is basically the same used by Le Jan and
Sznitman for 3-d Navier--Stokes equations, which need
small initial data to work. In our much simpler setting
we are able to make this precise, finding all the cases
where their method fails to give the solution. The
second approach is based on a resummed representation,
which we can prove to give all the solutions of the
problem, even those with large initial data.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Barbato:2005:FIB,
author = "David Barbato",
title = "{FKG} Inequality for {Brownian} Motion and Stochastic
Differential Equations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "2:7--2:16",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1127",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1127",
abstract = "The purpose of this work is to study some possible
application of FKG inequality to the Brownian motion
and to Stochastic Differential Equations. We introduce
a special ordering on the Wiener space and prove the
FKG inequality with respect to this ordering. Then we
apply this result on the solutions $ X_t $ of a
stochastic differential equation with a positive
coefficient $ \sigma $ , we prove that these solutions
$ X_t $ are increasing with respect to the ordering,
and finally we deduce a correlation inequality between
the solution of different stochastic equations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Manstavicius:2005:NMP,
author = "Martynas Manstavicius",
title = "A Non-{Markovian} Process with Unbounded
$p$-Variation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "3:17--3:28",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1128",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1128",
abstract = "A recent theorem by M. Manstavicius (2004) provided a
link between a certain function of transition
probabilities of a strong Markov process and the
boundedness of the $p$-variation of its trajectories.
Here one assumption of that theorem is relaxed and an
example is constructed to show that the Markov property
cannot be easily dispensed with.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Marchal:2005:MCS,
author = "Philippe Marchal",
title = "Measure Concentration for Stable Laws with Index Close
to 2",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "4:29--4:35",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1129",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1129",
abstract = "We give upper bounds for the probability $ P(|f(X) - E
f(X)| > x) $, where $X$ is a stable random variable
with index close to 2 and $f$ is a Lipschitz function.
While the optimal upper bound is known to be of order $
1 / x^\alpha $ for large $x$, we establish, for smaller
$x$, an upper bound of order $ \exp ( - x^\alpha / 2)$,
which relates the result to the Gaussian
concentration.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Rassoul-Agha:2005:ZOL,
author = "Firas Rassoul-Agha",
title = "On the Zero--One Law and the Law of Large Numbers for
Random Walk in Mixing Random Environment",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "5:36--5:44",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1130",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1130",
abstract = "We prove a weak version of the law of large numbers
for multi-dimensional finite range random walks in
certain mixing elliptic random environments. This
already improves previously existing results, where a
law of large numbers was known only under strong enough
transience. We also prove that for such walks the
zero-one law implies a law of large numbers.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Hammond:2005:CEP,
author = "Alan Hammond",
title = "Critical Exponents in Percolation via Lattice
Animals",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "6:45--6:59",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1131",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1131",
abstract = "We examine the percolation model on $ \mathbb {Z}^d $
by an approach involving lattice animals and their
surface-area-to-volume ratio. For $ \beta \in [0, 2 (d
- 1)) $, let $ f(\beta) $ be the asymptotic exponential
rate in the number of edges of the number of lattice
animals containing the origin which have
surface-area-to-volume ratio $ \beta $. The function
$f$ is bounded above by a function which may be written
in an explicit form. For low values of $ \beta $ ($
\beta \leq 1 / p_c - 1$), equality holds, as originally
demonstrated by F. Delyon. For higher values ($ \beta >
1 / p_c - 1$), the inequality is strict.\par
We introduce two critical exponents, one of which
describes how quickly $f$ falls away from the explicit
form as $ \beta $ rises from $ 1 / p_c - 1$, and the
second of which describes how large clusters appear in
the marginally subcritical regime of the percolation
model. We demonstrate that the pair of exponents must
satisfy certain inequalities. Other such inequalities
yield sufficient conditions for the absence of an
infinite cluster at the critical value (c.f.
{citetechrep}). The first exponent is related to one of
a more conventional nature in the scaling theory of
percolation, that of correlation size. In deriving this
relation, we find that there are two possible
behaviours, depending on the value of the first
exponent, for the typical surface-area-to-volume ratio
of an unusually large cluster in the marginally
subcritical regime.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Ball:2005:PTM,
author = "Karen Ball",
title = "{Poisson} Thinning by Monotone Factors",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "7:60--7:69",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1134",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1134",
abstract = "Let $X$ and $Y$ be Poisson point processes on the real
numbers with rates $ l_1$ and $ l_2$ respectively. We
show that if $ l_1 > l_2$, then there exists a
deterministic map $f$ such that $ f(X)$ and $Y$ have
the same distribution, the joint distribution of $ (X,
f(X))$ is translation-invariant, and which is monotone
in the sense that for all intervals $I$, $ f(X)(I) \leq
X(I)$, almost surely.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Mason:2005:WDR,
author = "David Mason and Joel Zinn",
title = "When Does a Randomly Weighted Self-normalized Sum
Converge in Distribution?",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "8:70--8:81",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1135",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See acknowledgment of priority
\cite{Mason:2005:APW}.",
URL = "http://ecp.ejpecp.org/article/view/1135",
abstract = "We determine exactly when a certain randomly weighted,
self--normalized sum converges in distribution,
partially verifying a 1965 conjecture of Leo Breiman.
We, then, apply our results to characterize the
asymptotic distribution of relative sums and to provide
a short proof of a 1973 conjecture of Logan, Mallows,
Rice and Shepp on the asymptotic distribution of
self--normalized sums in the case of symmetry.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Carlsson:2005:SNT,
author = "Niclas Carlsson",
title = "Some Notes on Topological Recurrence",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "9:82--9:93",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1137",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1137",
abstract = "We review the concept of topological recurrence for
weak Feller Markov chains on compact state spaces and
explore the implications of this concept for the
ergodicity of the processes. We also prove some
conditions for existence and uniqueness of invariant
measures of certain types. Examples are given from the
class of iterated function systems on the real line.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Kozlova:2005:NOT,
author = "Marina Kozlova and Paavo Salminen",
title = "A Note on Occupation Times of Stationary Processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "10:94--10:104",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1138",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1138",
abstract = "Consider a real valued stationary process $ X = {X_s
:, s \in R} $. For a fixed $ t \in R $ and a set $D$ in
the state space of $X$, let $ g_t$ and $ d_t$ denote
the starting and the ending time, respectively, of an
excursion from and to $D$ (straddling $t$). Introduce
also the occupation times $ I^+_t$ and $ I^-_t$ above
and below, respectively, the observed level at time $t$
during such an excursion. In this note we show that the
pairs $ (I^+_t, I^-_t)$ and $ (t - g_t, d_t - t)$ are
identically distributed. This somewhat curious property
is, in fact, seen to be a fairly simple consequence of
the known general uniform sojourn law which implies
that conditionally on $ I^+_t + I^-_t = v$ the variable
$ I^+_t$ (and also $ I^-_t$) is uniformly distributed
on $ (0, v)$. We also particularize to the stationary
diffusion case and show, e.g., that the distribution of
$ I^-_t + I^+_t$ is a mixture of gamma distributions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Bodineau:2005:UPL,
author = "Thierry Bodineau and James Martin",
title = "A Universality Property for Last-Passage Percolation
Paths Close to the Axis",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "11:105--11:112",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1139",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1139",
abstract = "We consider a last-passage directed percolation model
in $ Z_+^2 $, with i.i.d. weights whose common
distribution has a finite $ (2 + p) $ th moment. We
study the fluctuations of the passage time from the
origin to the point $ (n, n^a) $. We show that, for
suitable $a$ (depending on $p$), this quantity,
appropriately scaled, converges in distribution as $ n
\to \infty $ to the Tracy-Widom distribution,
irrespective of the underlying weight distribution. The
argument uses a coupling to a Brownian directed
percolation problem and the strong approximation of
Koml{\'o}s, Major and Tusn{\'a}dy.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Kordzakhia:2005:EMH,
author = "George Kordzakhia",
title = "The Escape Model on a Homogeneous Tree",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "12:113--12:124",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1140",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1140",
abstract = "There are two types of particles interacting on a
homogeneous tree of degree $ d + 1 $. The particles of
the first type colonize the empty space with
exponential rate 1, but cannot take over the vertices
that are occupied by the second type. The particles of
the second type spread with exponential rate $ \lambda
$. They colonize the neighboring vertices that are
either vacant or occupied by the representatives of the
opposite type, and annihilate the particles of the type
1 as they reach them. There exists a critical value $
\lambda_c = (2 d - 1) + \sqrt {(2d - 1)^2 - 1} $ such
that the first type survives with positive probability
for $ \lambda < \lambda_c $, and dies out with
probability one for $ \lambda > \lambda_c $. We also
find the growth profile which characterizes the rate of
growth of the type 1 in the space-time on the event of
survival.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Conlon:2005:HND,
author = "Joseph Conlon and Ian Pilizzotto",
title = "On Homogenization of Non-Divergence Form Partial
Difference Equations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "13:125--13:135",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1141",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1141",
abstract = "In this paper a method for proving homogenization of
divergence form elliptic equations is extended to the
non-divergence case. A new proof of homogenization is
given when the coefficients in the equation are assumed
to be stationary and ergodic. A rate of convergence
theorem in homogenization is also obtained, under the
assumption that the coefficients are i.i.d. and the
elliptic equation can be solved by a convergent
perturbation series.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Hobson:2005:DBC,
author = "Tim Hobson and Rodge Tribe",
title = "On the Duality between Coalescing {Brownian} Particles
and the Heat Equation Driven by {Fisher--Wright}
Noise",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "14:136--14:145",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1143",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1143",
abstract = "This paper concerns the Markov process duality between
the one-dimensional heat equation driven by
Fisher-Wright white noise and slowly coalescing
Brownian particles. A representation is found for the
law of the solution $ x \to U(t, x) $ to the stochastic
PDE, at a fixed time, in terms of a labelled system of
such particles.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Kyprianou:2005:NSO,
author = "Andreas Kyprianou and Budhi Surya",
title = "On the {Novikov--Shiryaev} Optimal Stopping Problems
in Continuous Time",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "15:146--15:154",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1144",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1144",
abstract = "Novikov and Shiryaev (2004) give explicit solutions to
a class of optimal stopping problems for random walks
based on other similar examples given in Darling et al.
(1972). We give the analogue of their results when the
random walk is replaced by a L{\'e}vy process. Further
we show that the solutions show no contradiction with
the conjecture given in Alili and Kyprianou (2004) that
there is smooth pasting at the optimal boundary if and
only if the boundary of the stopping region is
irregular for the interior of the stopping region.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Panchenko:2005:QAP,
author = "Dmitriy Panchenko",
title = "A Question about the {Parisi} Functional",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "16:155--16:166",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1145",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1145",
abstract = "We conjecture that the Parisi functional in the SK
model is convex in the functional order parameter and
prove a partial result that shows the convexity along
one-sided directions. A consequence of this result is
the log-convexity of $ L_m $ norm for a class or random
variables.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Angel:2005:JPB,
author = "Omer Angel and Alexander Holroyd and James Martin",
title = "The Jammed Phase of the {Biham--Middleton--Levine}
Traffic Model",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "17:167--17:178",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1148",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1148",
abstract = "Initially a car is placed with probability $p$ at each
site of the two-dimensional integer lattice. Each car
is equally likely to be East-facing or North-facing,
and different sites receive independent assignments. At
odd time steps, each North-facing car moves one unit
North if there is a vacant site for it to move into. At
even time steps, East-facing cars move East in the same
way. We prove that when $p$ is sufficiently close to 1
traffic is jammed, in the sense that no car moves
infinitely many times. The result extends to several
variant settings, including a model with cars moving at
random times, and higher dimensions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Caravenna:2005:CAB,
author = "Francesco Caravenna and Giambattista Giacomin",
title = "On Constrained Annealed Bounds for Pinning and Wetting
Models",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "18:179--18:189",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1150",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1150",
abstract = "The free energy of quenched disordered systems is
bounded above by the free energy of the corresponding
annealed system. This bound may be improved by applying
the annealing procedure, which is just Jensen
inequality, after having modified the Hamiltonian in a
way that the quenched expressions are left unchanged.
This procedure is often viewed as a partial annealing
or as a constrained annealing, in the sense that the
term that is added may be interpreted as a Lagrange
multiplier on the disorder variables.\par
In this note we point out that, for a family of models,
some of which have attracted much attention, the
multipliers of the form of empirical averages of local
functions cannot improve on the basic annealed bound
from the viewpoint of characterizing the phase diagram.
This class of multipliers is the one that is suitable
for computations and it is often believed that in this
class one can approximate arbitrarily well the quenched
free energy.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Catuogno:2005:GSD,
author = "Pedro Catuogno and Paulo Ruffino",
title = "Geometry of Stochastic Delay Differential Equations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "19:190--19:195",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1151",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1151",
abstract = "Stochastic delay differential equations (SDDE) on a
manifold $M$ depend intrinsically on a connection $
\nabla $ in this space. The main geometric result in
this notes concerns the horizontal lift of solutions of
SDDE on a manifold $M$ to an SDDE in the frame bundle $
B M$, hence the lifted equation should come together
with the prolonged horizontal connection $ \nabla^H$ on
$ B M$. We show that every horizontal semimartingale
can be represented as a solution of an SDDE.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Khoshnevisan:2005:EVA,
author = "Davar Khoshnevisan and David Levin and Zhan Shi",
title = "An Extreme-Value Analysis of the {LIL} for {Brownian}
Motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "20:196--20:206",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1154",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1154",
abstract = "We use excursion theory and the ergodic theorem to
present an extreme-value analysis of the classical law
of the iterated logarithm (LIL) for Brownian motion. A
simplified version of our method also proves, in a
paragraph, the classical theorem of Darling and
Erd{\H{o}}s (1956).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Hashorva:2005:BCB,
author = "Enkelejd Hashorva",
title = "Boundary Crossings of {Brownian} Motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "21:207--21:217",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1155",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1155",
abstract = "Let $B$ be a standard Brownian motion and let $
b_\gamma $ be a piecewise linear continuous boundary
function. In this paper we obtain an exact asymptotic
expansion of $ P \{ B(t) < b_\gamma (t), \forall t \in
[0, 1] \} $ provided that the boundary function
satisfies $ \lim_{\gamma \to \infty } b_\gamma (t^*) =
- \infty $ for some $ t^* \in (0, 1]$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Chobanyan:2005:SLL,
author = "Sergei Chobanyan and Shlomo Levental and Habib
Salehi",
title = "Strong Law of Large Numbers Under a General Moment
Condition",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "22:218--22:222",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1156",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1156",
abstract = "We use our maximum inequality for $p$-th order random
variables ($ p > 1$) to prove a strong law of large
numbers (SLLN) for sequences of $p$-th order random
variables. In particular, in the case $ p = 2$ our
result shows that $ \sum f(k) / k < \infty $ is a
sufficient condition for SLLN for $f$-quasi-stationary
sequences. It was known that the above condition, under
the additional assumption of monotonicity of $f$,
implies SLLN (Erdos (1949), Gal and Koksma (1950),
Gaposhkin (1977), Moricz (1977)). Besides getting rid
of the monotonicity condition, the inequality enables
us to extend the general result to $p$-th order random
variables, as well as to the case of
Banach-space-valued random variables.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Handa:2005:SFS,
author = "Kenji Handa",
title = "Sampling Formulae for Symmetric Selection",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "23:223--23:234",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1159",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1159",
abstract = "We study partition distributions in a population
genetics model incorporating symmetric selection and
mutation. They generalize Ewens distributions in the
infinitely-many-neutral-alleles model, an explicit
expression of which is known as the Ewens sampling
formula. A sampling formula for the generalized model
is obtained by means of calculus for Poisson and gamma
processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Liao:2005:MRB,
author = "Ming Liao and Longmin Wang",
title = "Motion of a Rigid Body under Random Perturbation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "24:235--24:243",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1163",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1163",
abstract = "We use stochastic analysis to study the random motion
of a rigid body under a white noise perturbation. We
obtain a formula for the angular velocity in an average
sense and discuss the stability near a principle
axis.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Roitershtein:2005:LSL,
author = "Alexander Roitershtein",
title = "A Log-scale Limit Theorem for One-dimensional Random
Walks in Random Environments",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "25:244--25:253",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1164",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1164",
abstract = "We consider a transient one-dimensional random walk $
X_n $ in random environment having zero asymptotic
speed. For a class of non-i.i.d. environments we show
that $ \log X_n / \log n $ converges in probability to
a positive constant.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Istas:2005:SHF,
author = "Jacques Istas",
title = "Spherical and Hyperbolic Fractional {Brownian}
Motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "26:254--26:262",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1166",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1166",
abstract = "We define a Fractional Brownian Motion indexed by a
sphere, or more generally by a compact rank one
symmetric space, and prove that it exists if, and only
if, $ 0 < H \leq 1 / 2 $. We then prove that Fractional
Brownian Motion indexed by an hyperbolic space exists
if, and only if, $ 0 < H \leq 1 / 2 $. At last, we
prove that Fractional Brownian Motion indexed by a real
tree exists when $ 0 < H \leq 1 / 2 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Popov:2005:RWA,
author = "Serguei Popov and Marina Vachkovskaia",
title = "Random Walk Attracted by Percolation Clusters",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "27:263--27:272",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1167",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1167",
abstract = "Starting with a percolation model in $ \mathbb {Z}^d $
in the subcritical regime, we consider a random walk
described as follows: the probability of transition
from $x$ to $y$ is proportional to some function $f$ of
the size of the cluster of $y$. This function is
supposed to be increasing, so that the random walk is
attracted by bigger clusters. For $ f(t) = e^{\beta t}$
we prove that there is a phase transition in $ \beta $,
i.e., the random walk is subdiffusive for large $ \beta
$ and is diffusive for small $ \beta $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Khan:2005:LLR,
author = "T{\"a}mur Khan and Luc Devroye and Ralph Neininger",
title = "A Limit Law for the Root Value of Minimax Trees",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "28:273--28:281",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1168",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1168",
abstract = "We consider minimax trees with independent,
identically distributed leaf values that have a
continuous distribution function $ F_V $ being strictly
increasing on the range where $ 0 < F_V < 1 $. It was
shown by Pearl that the root value of such trees
converges to a deterministic limit in probability
without any scaling. We show that after normalization
we have convergence in distribution to a nondegenerate
limit random variable.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Roch:2005:BFM,
author = "S{\'e}bastien Roch",
title = "Bounding Fastest Mixing",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "29:282--29:296",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1169",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1169",
abstract = "In a recent work, Boyd, Diaconis and Xiao introduced a
semidefinite programming approach for computing the
fastest mixing Markov chain on a graph of allowed
transitions, given a target stationary distribution. In
this paper, we show that standard mixing time analysis
techniques---variational characterizations,
conductance, canonical paths---can be used to give
simple, nontrivial lower and upper bounds on the
fastest mixing time. To test the applicability of this
idea, we consider several detailed examples including
the Glauber dynamics of the Ising model.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Mason:2005:APW,
author = "David Mason and Joel Zinn",
title = "Acknowledgment of Priority: {When Does a Randomly
Weighted Self-normalized Sum Converge in Distribution?
(\booktitle{Elect. Comm. in Probab.} {\bf 10} (2005),
70--81)}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "10",
pages = "30:297--30:297",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v10-1170",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See \cite{Mason:2005:WDR}.",
URL = "http://ecp.ejpecp.org/article/view/1170",
abstract = "Christian Houdre has kindly pointed us to a paper by
A. Fuks, A. Joffe and J. Teugels, where their Theorem
5.3 is our Proposition 3 in the case $ 0 < \alpha < 1
$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Taniguchi:2006:QWF,
author = "Setsuo Taniguchi",
title = "On the Quadratic {Wiener} Functional Associated with
the {Malliavin} Derivative of the Square Norm of
{Brownian} Sample Path on Interval",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "1:1--1:10",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1174",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1174",
abstract = "Exact expressions of the stochastic oscillatory
integrals with the phase function, which is the
quadratic Wiener functional obtained from the Malliavin
derivative of the square norm of the Brownian sample
path on interval, are given. As an application, the
density function of the distribution of the half of the
Wiener functional is given.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Balan:2006:SAM,
author = "Raluca Balan and Ingrid-Mona Zamfirescu",
title = "Strong Approximation for Mixing Sequences with
Infinite Variance",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "2:11--2:23",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1175",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1175",
abstract = "In this paper we prove a strong approximation result
for a mixing sequence with infinite variance and
logarithmic decay rate of the mixing coefficient. The
result is proved under the assumption that the
distribution is symmetric and lies in the domain of
attraction of the normal law. Moreover the truncated
variance function is supposed to be slowly varying with
log-log type remainder.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Gaans:2006:IMS,
author = "Onno Gaans and Jan Neerven",
title = "Invariant measures for stochastic {Cauchy} problems
with asymptotically unstable drift semigroup",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "3:24--3:34",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1184",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1184",
abstract = "We investigate existence and permanence properties of
invariant measures for abstract stochastic Cauchy
problems of the form\par
$$ d U(t) = (A U(t) + f) \, d t + B \, d W_H(t), \ \ t
\ge 0, $$
governed by the generator $A$ of an asymptotically
unstable $ C_0$-semigroup on a Banach space $E$. Here $
f \in E$ is fixed, $ W_H$ is a cylindrical Brownian
motion over a separable real Hilbert space $H$, and $B$
is a bounded operator from $H$ to $E$. We show that if
$E$ does not contain a copy of $ c_0$, such invariant
measures fail to exist generically but may exist for a
dense set of operators $B$. It turns out that many
results on invariant measures which hold under the
assumption of uniform exponential stability of $S$
break down without this assumption.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Invariant measures, stochastic evolution equations in
Hilbert spaces",
}
@Article{Dacunha-Castelle:2006:DLM,
author = "Didier Dacunha-Castelle and Lisandro Fermin",
title = "Disaggregation of Long Memory Processes on $ \mathcal
{C}^{\infty } $ Class",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "4:35--4:44",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1133",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1133",
abstract = "We prove that a large set of long memory (LM)
processes (including classical LM processes and all
processes whose spectral densities have a countable
number of singularities controlled by exponential
functions) are obtained by an aggregation procedure
involving short memory (SM) processes whose spectral
densities are infinitely differentiable ($ C^\infty $).
We show that the $ C^\infty $ class of spectral
densities infinitely differentiable is the best class
to get a general result for disaggregation of LM
processes in SM processes, in the sense that the result
given in $ C^\infty $ class cannot be improved by
taking for instance analytic functions instead of
indefinitely derivable functions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Aggregation; disaggregation; long memory process;
mixture.",
}
@Article{Kontoyiannis:2006:MCC,
author = "Ioannis Kontoyiannis and Mokshay Madiman",
title = "Measure Concentration for Compound {Poisson}
Distributions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "5:45--5:57",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1190",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1190",
abstract = "We give a simple development of the concentration
properties of compound Poisson measures on the
nonnegative integers. A new modification of the Herbst
argument is applied to an appropriate modified
logarithmic-Sobolev inequality to derive new
concentration bounds. When the measure of interest does
not have finite exponential moments, these bounds
exhibit optimal {em polynomial} decay. Simple new
proofs are also given for earlier results of Houdr{\'e}
(2002) and Wu (2000).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Compound Poisson measure; entropy method; Herbst
argument; logarithmic-Sobolev inequality; measure
concentration; polynomial tails",
}
@Article{Andrew:2006:PFP,
author = "Peter Andrew",
title = "A Proof from `First Principles' of {Kesten}'s Result
for the Probabilities with which a Subordinator Hits
Points",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "6:58--6:63",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1193",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1193",
abstract = "We give a simpler and shorter proof of Kesten's result
for the probabilities with which a subordinator hits
points.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "L{\'e}vy processes, subordinators, hitting
probabilities",
}
@Article{Gozlan:2006:ICT,
author = "Nathael Gozlan",
title = "Integral criteria for transportation cost
inequalities",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "7:64--7:77",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1198",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1198",
abstract = "Abstract. In this paper, we provide a characterization
of a large class of transportation-cost inequalities in
terms of exponential integrability of the cost function
under the reference probability measure. Our results
completely extend the previous works by Djellout,
Guillin and Wu (DGW03) and Bolley and Villani (BV03).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Transportation-cost inequalities and Orlicz Spaces",
}
@Article{Andersson:2006:VFN,
author = "Jenny Andersson and Olle H{\"a}ggstr{\"o}m and
Marianne M{\aa}nsson",
title = "The volume fraction of a non-overlapping germ--grain
model",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "8:78--8:88",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1197",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1197",
abstract = "We discuss the volume fraction of a model of
non-overlapping convex grains. It is obtained from
thinning a Poisson process where each point has a
weight and is the centre of a grain, by removing any
grain that is overlapped by one of larger or equal
weight. In the limit as the intensity of the Poisson
process tends to infinity, the model can be identified
with the intact grains in the dead leaves model if the
weights are independent of the grain sizes. In this
case we can show that the volume fraction is at most $
1 / 2^d $ for $ d = 1 $ or $2$ if the shape is fixed,
but the size and the orientation are random. The upper
bound is achieved for centrally symmetric sets of the
same size and orientation. For general $d$ we can show
the upper bound, $ 1 / 2^d$, for spherical grains with
two--point radius distribution. If dependence between
weight and size is allowed, it is possible to achieve a
volume fraction arbitrarily close to one.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "volume fraction, germ-grain model, dead leaves model",
}
@Article{Weerasinghe:2006:CSG,
author = "Ananda Weerasinghe",
title = "A Controller And A Stopper Game With Degenerate
Variance Control",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "9:89--9:99",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1202",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1202",
abstract = "We consider a zero sum stochastic differential game
which involves two players, {\em the controller\/} and
{\em the stopper}. The stopper selects the stopping
rule which halts the game. The controller chooses the
diffusion coefficient of the corresponding state
process which is allowed to degenerate. At the end of
the game, the controller pays the stopper, the amount $
E \int_0^{\tau } e^{- \alpha t} C(Z_x(t))d t $, where $
Z_x(\cdot) $ represents the state process with initial
position $x$ and $ \alpha $ is a positive constant.
Here $ C(\cdot)$ is a reward function where the set $
\{ x : C(x) > 0 \} $ is an open interval which contains
the origin. Under some assumptions on the reward
function $ C(\cdot)$ and the drift coefficient of the
state process, we show that this game has a value.
Furthermore, this value function is Lipschitz
continuous, but it fails to be a $ C^1$ function.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "stochastic games, optimal stopping, degenerate
diffusions, saddle point",
}
@Article{Benjamini:2006:RWW,
author = "Itai Benjamini and Gady Kozma and Dan Romik",
title = "Random walks with $k$-wise independent increments",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "10:100--10:107",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1201",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1201",
abstract = "We construct examples of a random walk with
pairwise-independent steps which is almost surely
bounded, and for any m and k a random walk with k-wise
independent steps which has no stationary distribution
modulo m.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "pairwise independence; pseudo-randomness;
quasi-randomness; Random walk",
}
@Article{Khoshnevisan:2006:NFP,
author = "Davar Khoshnevisan and Paavo Salminen and Marc Yor",
title = "A note on a.s. finiteness of perpetual integral
functionals of diffusions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "11:108--11:117",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1203",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1203",
abstract = "In this note we use the boundary classification of
diffusions in order to derive a criterion for the
convergence of perpetual integral functionals of
transient real-valued diffusions. We present a second
approach, based on Khas'minskii's lemma, which is
applicable also to spectrally negative L{\'e}vy
processes. In the particular case of transient Bessel
processes, our criterion agrees with the one obtained
via Jeulin's convergence lemma.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion, random time change, exit boundary,
local time, additive functional, stochastic
differential equation, Khas'minskii's lemma, spectrally
negative L{\'e}vy process.",
}
@Article{Zerner:2006:RTE,
author = "Martin Zerner",
title = "Recurrence and transience of excited random walks on
{$ Z^d $} and strips",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "12:118--12:128",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1200",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1200",
abstract = "We investigate excited random walks on $ Z^d, d \ge 1,
$ and on planar strips $ Z \times {0, 1, \ldots, L - 1}
$ which have a drift in a given direction. The strength
of the drift may depend on a random i.i.d. environment
and on the local time of the walk. We give exact
criteria for recurrence and transience, thus
generalizing results by Benjamini and Wilson for
once-excited random walk on $ Z^d $ and by the author
for multi-excited random walk on $Z$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Excited Random Walk, Recurrence, Self-Interacting
Random Walk, Transience",
}
@Article{Chigansky:2006:RPF,
author = "Pavel Chigansky and Robert Liptser",
title = "On a role of predictor in the filtering stability",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "13:129--13:140",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1205",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1205",
abstract = "When is a nonlinear filter stable with respect to its
initial condition? In spite of the recent progress,
this question still lacks a complete answer in general.
Currently available results indicate that stability of
the filter depends on the signal ergodic properties and
the observation process regularity and may fail if
either of the ingredients is ignored. In this note we
address the question of stability in a particular weak
sense and show that the estimates of certain functions
are always stable. This is verified without dealing
directly with the filtering equation and turns to be
inherited from certain one-step predictor estimates.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "nonlinear filtering, stability, martingale
convergence",
}
@Article{Nicolas:2006:SSC,
author = "Fournier Nicolas",
title = "Standard stochastic coalescence with sum kernels",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "14:141--14:148",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1206",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1206",
abstract = "We build a Markovian system of particles entirely
characterized by their masses, in which each pair of
particles with masses $x$ and $y$ coalesce at rate $
K(x, y) \simeq x^\lambda + y^\lambda $, for some $
\lambda \in (0, 1)$, and such that the system is
initially composed of infinitesimally small
particles.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Coalescence, Stochastic interacting particle systems",
}
@Article{Dembo:2006:LMD,
author = "Amir Dembo and Qi-Man Shao",
title = "Large and Moderate Deviations for {Hotelling}'s {$ T^2
$}-Statistics",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "15:149--15:159",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1209",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1209",
abstract = "Let $ \mathbf {X}, \mathbf {X}_1, \mathbf {X}_2,
\ldots {} $ be i.i.d. $ \mathbb {R}^d$-valued random
variables. We prove large and moderate deviations for
Hotelling's $ T^2$-statistic when $ \mathbf {X}$ is in
the generalized domain of attraction of the normal
law.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "$T^2$ statistic; large deviation; law of the iterated
logarithm; moderate deviation; self-normalized partial
sums",
}
@Article{Pimentel:2006:TCC,
author = "Leandro Pimentel",
title = "The time constant and critical probabilities in
percolation models",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "16:160--16:167",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1210",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1210",
abstract = "We consider a first-passage percolation (FPP) model on
a Delaunay triangulation $ \mathcal {D} $ of the plane.
In this model each edge $ \mathbf {e} $ of $ \mathcal
{D} $ is independently equipped with a nonnegative
random variable $ \tau_{\mathbf {e}} $, with
distribution function $ \mathbb {F} $, which is
interpreted as the time it takes to traverse the edge.
Vahidi-Asl and Wierman \cite{VW90} have shown that,
under a suitable moment condition on $ \mathbb {F} $,
the minimum time taken to reach a point $ \mathbf {x} $
from the origin $ \mathbf {0} $ is asymptotically $ \mu
(\mathbb {F})| \mathbf {x}| $, where $ \mu (\mathbb
{F}) $ is a nonnegative finite constant. However the
exact value of the time constant $ \mu (\mathbb {F}) $
still a fundamental problem in percolation theory. Here
we prove that if $ \mathbb {F}(0) < 1 - p_c^* $ then $
\mu (\mathbb {F}) > 0 $, where $ p_c^* $ is a critical
probability for bond percolation on the dual graph $
\mathcal {D}^* $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "critical probabilities; Delaunay triangulations;
Percolation; time constant",
}
@Article{Steif:2006:SRP,
author = "Jeffrey Steif and Aidan Sudbury",
title = "Some results for poisoning in a catalytic model",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "17:168--17:177",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1211",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1211",
abstract = "We obtain new results concerning poisoning\slash
nonpoisoning in a catalytic model which has previously
been introduced and studied. We show that poisoning can
occur even when the arrival rate of one gas is smaller
than the sum of the arrival rates of the other gases,
and that poisoning does not occur when all gases have
equal arrival rates.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Interacting particle systems, catalytic model.",
}
@Article{Bass:2006:PUR,
author = "Richard Bass and Krzysztof Burdzy",
title = "Pathwise uniqueness for reflecting {Brownian} motion
in certain planar {Lipschitz} domains",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "18:178--18:181",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1213",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1213",
abstract = "We give a simple proof that in a Lipschitz domain in
two dimensions with Lipschitz constant one, there is
pathwise uniqueness for the Skorokhod equation
governing reflecting Brownian motion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "reflecting Brownian motion",
}
@Article{Vadlamani:2006:GGU,
author = "Sreekar Vadlamani and Robert Adler",
title = "Global geometry under isotropic {Brownian} flows",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "19:182--19:192",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1212",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1212",
abstract = "We consider global properties of a codimension one
manifold embedded in Euclidean space, as it evolves
under an isotropic and volume preserving Brownian flow
of diffeomorphisms. In particular, we obtain
expressions describing the expected rate of growth of
the Lipschitz-Killing curvatures, or intrinsic volumes,
of the manifold under the flow. These results shed new
light on some of the intriguing growth properties of
flows from a global perspective, rather than the local
perspective, on which there is a much larger
literature.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian flows; evolution equations; Lipschitz-Killing
curvatures; Lyapunov exponents.; manifolds; Stochastic
flows",
}
@Article{deLaFortelle:2006:SFL,
author = "Arnaud {de La Fortelle}",
title = "{Yule} Process sample path asymptotics",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "20:193--20:199",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1215",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1215",
abstract = "This paper presents two results on sample paths for
the Yule process: one fluid limit theorem and one
sample path large deviation result. The main interest
is to understand the way large deviation occurs in the
case of non-homogeneous processes. There are indeed two
new phenomena. First there is no ``typical'' speed of
large deviation. Second, the large deviation event is
concentrated on a finite interval of time.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Large deviations, random trees, branching process,
fluid limit, Yule process, martingale, change of
measure",
}
@Article{Kuelske:2006:SFL,
author = "Christof Kuelske and Enza Orlandi",
title = "A simple fluctuation lower bound for a disordered
massless random continuous spin model in $ d = 2 $",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "21:200--21:205",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1218",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1218",
abstract = "We prove a finite volume lower bound of the order $
\sqrt {\log N} $ on the delocalization of a disordered
continuous spin model (resp. effective interface model)
in $ d = 2 $ in a box of size $N$. The interaction is
assumed to be massless, possibly anharmonic and
dominated from above by a Gaussian. Disorder is
entering via a linear source term. For this model
delocalization with the same rate is proved to take
place already without disorder. We provide a bound that
is uniform in the configuration of the disorder, and so
our proof shows that disorder will only enhance
fluctuations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Interfaces, quenched systems, continuous spin models,
entropy inequality",
}
@Article{Tevzadze:2006:EME,
author = "Revaz Tevzadze and Mikhael Mania",
title = "An Exponential Martingale Equation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "22:206--22:216",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1220",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1220",
abstract = "We prove an existence of a unique solution of an
exponential martingale equation in the class of BMO
martingales. The solution is used to characterize
optimal martingale measures.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Backward stochastic differential equation, exponential
martingale, martingale measures",
}
@Article{Yang:2006:SPH,
author = "Ming Yang",
title = "A short proof of the {Hausdorff} dimension formula for
{L{\'e}vy} processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "23:217--23:219",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1199",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1199",
abstract = "A different but very short proof of a recent result of
Khoshnevisan.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Hausdorff dimension",
}
@Article{Major:2006:MVH,
author = "Peter Major",
title = "A multivariate version of {Hoeffding}'s inequality",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "24:220--24:229",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1221",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1221",
abstract = "In this paper a multivariate version of Hoeffding's
inequality is proved about the tail distribution of
homogeneous polynomials of Rademacher functions with an
optimal constant in the exponent of the upper bound.
The proof is based on an estimate about the moments of
homogeneous polynomials of Rademacher functions which
can be considered as an improvement of Borell's
inequality in a most important special case.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Hoeffding's inequality, Borell's inequality, multiple
Wiener--It{\^o} integrals, diagram formula",
}
@Article{Fitzsimmons:2006:ERE,
author = "Patrick Fitzsimmons",
title = "On the Existence of Recurrent Extensions of
Self-similar {Markov} Processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "25:230--25:241",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1222",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1222",
abstract = "Let $ X = (X_t)_{t \geq 0} $ be a self-similar Markov
process with values in the non-negative half-line, such
that the state $0$ is a trap. We present a necessary
and sufficient condition for the existence of a
self-similar recurrent extension of $X$ that leaves $0$
continuously. This condition is expressed in terms of
the L{\'e}vy process associated with $X$ by the
Lamperti transformation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "self-similar, semi-stable, Lamperti transformation,
recurrent extension, Cram{\'e}r condition, excursion",
}
@Article{Istas:2006:FFI,
author = "Jacques Istas",
title = "On Fractional Fields indexed by Metric Spaces",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "26:242--26:251",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1223",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1223",
abstract = "We define and build $H$-fractional $ \alpha $-stable
fields indexed by a metric space $ (E, d)$. We mainly
apply these results to spheres, hyperbolic spaces and
real trees.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Fractional Stable Fields, Metric Spaces",
}
@Article{LeGall:2006:OMS,
author = "Jean-Fran{\c{c}}ois {Le Gall} and Mathieu Merle",
title = "On the occupation measure of super-{Brownian} motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "27:252--27:265",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1225",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1225",
abstract = "We derive the asymptotic behavior of the total
occupation measure of the unit ball for super-Brownian
motion started from the Dirac measure at a distant
point and conditioned to hit the unit ball. In the
critical dimension 4, we obtain a limiting exponential
distribution.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "super-Brownian motion, occupation measure, limit
distribution",
}
@Article{Rueschendorf:2006:ETB,
author = "Ludger Rueschendorf and Eva-Maria Schopp",
title = "Exponential tail bounds for max-recursive sequences",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "28:266--28:277",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1227",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1227",
abstract = "Exponential tail bounds are derived for solutions of
max-recursive equations and for max-recursive random
sequences, which typically arise as functionals of
recursive structures, of random trees or in recursive
algorithms. In particular they arise in the worst case
analysis of divide and conquer algorithms, in parallel
search algorithms or in the height of random tree
models. For the proof we determine asymptotic bounds
for the moments or for the Laplace transforms and apply
a characterization of exponential tail bounds due to
Kasahara (1978).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "recursive algorithm, exponential bounds, divide and
conquer algorithm, probabilistic analysis of
algorithms",
}
@Article{Evans:2006:ENZ,
author = "Steven Evans",
title = "The expected number of zeros of a random system of
$p$-adic polynomials",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "29:278--29:290",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1230",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1230",
abstract = "We study the simultaneous zeros of a random family of
$d$ polynomials in $d$ variables over the $p$-adic
numbers. For a family of natural models, we obtain an
explicit constant for the expected number of zeros that
lie in the $d$-fold Cartesian product of the $p$-adic
integers. Considering models in which the maximum
degree that each variable appears is $N$, this expected
value is\par
$$ p^{d \lfloor \log_p N \rfloor } \left (1 + p^{-1} +
p^{-2} + \cdots + p^{-d} \right)^{-1} $$
for the simplest such model.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "co-area formula, Kac-Rice formula, local field,
Gaussian, $q$-binomial formula, random matrix",
}
@Article{Kondo:2006:SPE,
author = "Hitoshi Kondo and Makoto Maejima and Ken-iti Sato",
title = "Some properties of exponential integrals of {L{\'e}vy}
processes and examples",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "30:291--30:303",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1232",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1232",
abstract = "The improper stochastic integral $ Z = \int_0^{\infty
-} \exp ( - X_{s-})d Y_s $ is studied, where $ { (X_t,
Y_t), t \geq 0 } $ is a L{\'e}vy process on $ R^{1 + d}
$ with $ {X_t } $ and $ {Y_t } $ being $R$-valued and $
R^d$-valued, respectively. The condition for existence
and finiteness of $Z$ is given and then the law $ {\cal
L}(Z)$ of $Z$ is considered. Some sufficient conditions
for $ {\cal L}(Z)$ to be selfdecomposable and some
sufficient conditions for $ {\cal L}(Z)$ to be
non-selfdecomposable but semi-selfdecomposable are
given. Attention is paid to the case where $ d = 1$, $
{X_t}$ is a Poisson process, and $ {X_t}$ and $ {Y_t}$
are independent. An example of $Z$ of type $G$ with
selfdecomposable mixing distribution is given",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Generalized Ornstein--Uhlenbeck process, L{\'e}vy
process, selfdecomposability, semi-selfdecomposability,
stochastic integral",
}
@Article{Duerre:2006:UMD,
author = "Maximilian Duerre",
title = "Uniqueness of multi-dimensional infinite volume
self-organized critical forest-fire models",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "31:304--31:315",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1229",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1229",
abstract = "In a forest-fire model, each site of the square
lattice is either vacant or occupied by a tree. Vacant
sites get occupied according to independent rate 1
Poisson processes. Independently at each site ignition
occurs according to independent rate lambda Poisson
processes. When a site is hit by ignition, then its
whole occupied cluster becomes vacant instantaneously.
The article studies whether a multi-dimensional
infinite volume forest-fire process with given
parameter is unique. Under an assumption on the decay
of the cluster size distribution, a process that
dominates the forest-fire process is used to show
uniqueness. If lambda is big enough, then subcritical
site percolation shows the correctness of the
assumption",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "adapted; forest-fire model; forest-fires;
self-organized criticality; unique",
}
@Article{Alabert:2006:LSD,
author = "Aureli Alabert and Marco Ferrante",
title = "Linear stochastic differential-algebraic equations
with constant coefficients",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "32:316--32:335",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1236",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1236",
abstract = "We consider linear stochastic differential-algebraic
equations with constant coefficients and additive white
noise. Due to the nature of this class of equations,
the solution must be defined as a generalised process
(in the sense of Dawson and Fernique). We provide
sufficient conditions for the law of the variables of
the solution process to be absolutely continuous with
respect to Lebesgue measure.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stochastic differential-algebraic equations, Random
distributions",
}
@Article{Deijfen:2006:SRG,
author = "Maria Deijfen and Johan Jonasson",
title = "Stationary random graphs on {$Z$} with prescribed iid
degrees and finite mean connections",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "33:336--33:346",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1239",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1239",
abstract = "Let $F$ be a probability distribution with support on
the non-negative integers. A model is proposed for
generating stationary simple graphs on $Z$ with degree
distribution $F$ and it is shown for this model that
the expected total length of all edges at a given
vertex is finite if $F$ has finite second moment. It is
not hard to see that any stationary model for
generating simple graphs on $Z$ will give infinite mean
for the total edge length per vertex if $F$ does not
have finite second moment. Hence, finite second moment
of $F$ is a necessary and sufficient condition for the
existence of a model with finite mean total edge
length.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "degree distribution; Random graphs; stationary model",
}
@Article{Hildebrand:2006:CDG,
author = "Martin Hildebrand",
title = "On the {Chung--Diaconis--Graham} random process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "11",
pages = "34:347--34:356",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v11-1237",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1237",
abstract = "Chung, Diaconis, and Graham considered random
processes of the form $ X_{n + 1} = 2 X_n + b_n \pmod p
$ where $ X_0 = 0 $, $p$ is odd, and $ b_n$ for $ n =
0, 1, 2, \dots $ are i.i.d. random variables on $ \{ -
1, 0, 1 \} $. If $ \Pr (b_n = - 1) = \Pr (b_n = 1) =
\beta $ and $ \Pr (b_n = 0) = 1 - 2 \beta $, they asked
which value of $ \beta $ makes $ X_n$ get close to
uniformly distributed on the integers mod $p$ the
slowest. In this paper, we extend the results of Chung,
Diaconis, and Graham in the case $ p = 2^t - 1$ to show
that for $ 0 < \beta \le 1 / 2$, there is no such value
of $ \beta $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random processes, discrete Fourier analysis",
}
@Article{Rokhlin:2007:MSP,
author = "Dmitry Rokhlin",
title = "Martingale selection problem and asset pricing in
finite discrete time",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "1:1--1:8",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1240",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1240",
abstract = "Given a set-valued stochastic process $ (V_t)_{t =
0}^T $, we say that the martingale selection problem is
solvable if there exists an adapted sequence of
selectors $ \xi_t \in V_t $, admitting an equivalent
martingale measure. The aim of this note is to
underline the connection between this problem and the
problems of asset pricing in general discrete-time
market models with portfolio constraints and
transaction costs. For the case of relatively open
convex sets $ V_t(\omega) $ we present effective
necessary and sufficient conditions for the solvability
of a suitably generalized martingale selection problem.
We show that this result allows to obtain
computationally feasible formulas for the price bounds
of contingent claims. For the case of currency markets
we also sketch a new proof of the first fundamental
theorem of asset pricing.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "martingale selection, arbitrage, price bounds,
constraints, transaction costs",
}
@Article{Lageraas:2007:PMC,
author = "Andreas Lager{\aa}s",
title = "A population model for {$ \Lambda $}-coalescents with
neutral mutations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "2:9--2:20",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1245",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1245",
abstract = "Bertoin and Le Gall (2003) introduced a certain
probability measure valued Markov process that
describes the evolution of a population, such that a
sample from this population would exhibit a genealogy
given by the so-called $ \Lambda $-coalescent, or
coalescent with multiple collisions, introduced
independently by Pitman (1999) and Sagitov (1999). We
show how this process can be extended to the case where
lineages can experience mutations. Regenerative
compositions enter naturally into this model, which is
somewhat surprising, considering a negative result by
M{\"o}hle (2007).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "coalescent; exchangeability; mutations; population
model; sampling formula",
}
@Article{Bose:2007:SNR,
author = "Arup Bose and Arnab Sen",
title = "Spectral norm of random large dimensional noncentral
{Toeplitz} and {Hankel} matrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "3:21--3:27",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1243",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1243",
abstract = "Suppose $ s_n $ is the spectral norm of either the
Toeplitz or the Hankel matrix whose entries come from
an i.i.d. sequence of random variables with positive
mean $ \mu $ and finite fourth moment. We show that $
n^{-1 / 2}(s_n - n \mu) $ converges to the normal
distribution in either case. This behaviour is in
contrast to the known result for the Wigner matrices
where $ s_n - n \mu $ is itself asymptotically
normal.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Large dimensional random matrix, eigenvalues, Wigner
matrix, Toeplitz matrix, Hankel matrix, spectral
norm.",
}
@Article{Iksanov:2007:PPW,
author = "Alex Iksanov and Martin M{\"o}hle",
title = "A probabilistic proof of a weak limit law for the
number of cuts needed to isolate the root of a random
recursive tree",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "4:28--4:35",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1253",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1253",
abstract = "We present a short probabilistic proof of a weak
convergence result for the number of cuts needed to
isolate the root of a random recursive tree. The proof
is based on a coupling related to a certain random
walk.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "coupling; random recursive tree; random walk; stable
limit",
}
@Article{Kargin:2007:PNC,
author = "Vladislav Kargin",
title = "A Proof of a Non-Commutative {Central Limit Theorem}
by the {Lindeberg} Method",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "5:36--5:50",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1250",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1250",
abstract = "A Central Limit Theorem for non-commutative random
variables is proved using the Lindeberg method. The
theorem is a generalization of the Central Limit
Theorem for free random variables proved by Voiculescu.
The Central Limit Theorem in this paper relies on an
assumption which is weaker than freeness.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "central limit theorem; free convolution; free
independence; free probability; Lindeberg method",
}
@Article{Huang:2007:NIP,
author = "Wei Huang and Li-Xin Zhang",
title = "A note on the invariance principle of the product of
sums of random variables",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "6:51--6:56",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1255",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1255",
abstract = "The central limit theorem for the product of sums of
various random variables has been studied in a variety
of settings. The purpose of this note is to show that
this kind of result is a corollary of the invariance
principle.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "central limit theorem; invariance of principle;
product of sums of r.v.",
}
@Article{Uemura:2007:EJT,
author = "Toshihiro Uemura",
title = "On an extension of jump-type symmetric {Dirichlet}
forms",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "7:57--7:65",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1256",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1256",
abstract = "We show that any element from the ($ L^2$-)maximal
domain of a jump-type symmetric Dirichlet form can be
approximated by test functions under some conditions.
This gives us a direct proof of the fact that the test
functions is dense in Bessel potential spaces.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "extended Dirichlet space; jump-type Dirichlet form;
Siverstein extension",
}
@Article{Kuwada:2007:COK,
author = "Kazumasa Kuwada and Karl-Theodor Sturm",
title = "A counterexample for the optimality of
{Kendall--Cranston} coupling",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "8:66--8:72",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1160",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1160",
abstract = "We construct a Riemannian manifold where the
Kendall--Cranston coupling of two Brownian particle
does not maximize the coupling probability.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion; Kendall--Cranston coupling; manifold;
optimal coupling",
}
@Article{Bourgade:2007:EFP,
author = "Paul Bourgade and Takahiko Fujita and Marc Yor",
title = "{Euler}'s formulae for $ \zeta (2 n) $ and products of
{Cauchy} variables",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "9:73--9:80",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1244",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1244",
abstract = "We show how to recover Euler's formula for $ \zeta (2
n) $, as well as $ L_{\chi_4}(2 n + 1) $, for any
integer $n$, from the knowledge of the density of the
product $ \mathbb {C}_1, \mathbb {C}_2 \ldots, \mathbb
{C}_k$, for any $ k \geq 1$, where the $ \mathbb
{C}_i$'s are independent standard Cauchy variables.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Cauchy variables, stable variables, planar Brownian
motion, Euler numbers.",
}
@Article{Harris:2007:SPB,
author = "John Harris and Simon Harris",
title = "Survival probabilities for branching {Brownian} motion
with absorption",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "10:81--10:92",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1259",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1259",
abstract = "We study a branching Brownian motion (BBM) with
absorption, in which particles move as Brownian motions
with drift $ - \rho $, undergo dyadic branching at rate
$ \beta > 0 $, and are killed on hitting the origin. In
the case $ \rho > \sqrt {2 \beta } $ the extinction
time for this process, $ \zeta $, is known to be finite
almost surely. The main result of this article is a
large-time asymptotic formula for the survival
probability $ P^x(\zeta > t) $ in the case $ \rho >
\sqrt {2 \beta } $, where $ P^x $ is the law of the BBM
with absorption started from a single particle at the
position $ x > 0 $. We also introduce an additive
martingale, $V$, for the BBM with absorption, and then
ascertain the convergence properties of $V$. Finally,
we use $V$ in a `spine' change of measure and interpret
this in terms of `conditioning the BBM to survive
forever' when $ \rho > \sqrt {2 \beta }$, in the sense
that it is the large $t$-limit of the conditional
probabilities $ P^x(A \mid \zeta > t + s)$, for $ A \in
F_s$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "additive martingales.; Branching Brownian motion with
absorption; spine constructions",
}
@Article{Bose:2007:MCE,
author = "Arup Bose and Amites Dasgupta and Krishanu Maulik",
title = "Maxima of the cells of an equiprobable multinomial",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "11:93--11:105",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1260",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1260",
abstract = "Consider a sequence of multinomial random vectors with
increasing number of equiprobable cells. We show that
if the number of trials increases fast enough, the
sequence of maxima of the cells after a suitable
centering and scaling converges to the Gumbel
distribution. While results are available for maxima of
triangular arrays of independent random variables with
certain types of distribution, such results in a
dependent setup is new. We also prove that the maxima
of a triangular sequence of appropriate Binomial random
variables have the same limit distribution. An
auxiliary large deviation result for multinomial
distribution with increasing number of equiprobable
cells may also be of independent interest.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "limit distribution; maxima; Random sequences;
triangular array",
}
@Article{Saintier:2007:GST,
author = "Nicolas Saintier",
title = "A general stochastic target problem with jump
diffusion and an application to a hedging problem for
large investors",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "12:106--12:119",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1261",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1261",
abstract = "Let $ Z(t, z) $ be a $ \mathbb {R}^d$-valued
controlled jump diffusion starting from the point $z$
at time $t$. The aim of this paper is to characterize
the set $ V(t)$ of initial conditions $z$ such that $
Z(t, z)$ can be driven into a given target at a given
time. We do this by proving that the characteristic
function of the complement $ V(t)$ satisfies some
partial differential equation in the viscosity sense.
As an application, we study the problem of hedging in a
financial market with a large investor.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "jump diffusion; large investor; mathematical finance;
Stochastic control; viscosity solutions",
}
@Article{Spitzner:2007:AVF,
author = "Dan Spitzner and Thomas Boucher",
title = "Asymptotic variance of functionals of discrete-time
{Markov} chains via the {Drazin} inverse",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "13:120--13:133",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1262",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1262",
abstract = "We consider a $ \psi $-irreducible, discrete-time
Markov chain on a general state space with transition
kernel $P$. Under suitable conditions on the chain,
kernels can be treated as bounded linear operators
between spaces of functions or measures and the Drazin
inverse of the kernel operator $ I - P$ exists. The
Drazin inverse provides a unifying framework for
objects governing the chain. This framework is applied
to derive a computational technique for the asymptotic
variance in the central limit theorems of univariate
and higher-order partial sums. Higher-order partial
sums are treated as univariate sums on a
`sliding-window' chain. Our results are demonstrated on
a simple AR(1) model and suggest a potential for
computational simplification.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "$f$-regularity; asymptotic variance; Drazin inverse;
fundamental matrix; General state space Markov chains;
Markov chain central limit theorem",
}
@Article{DeBlassie:2007:CLL,
author = "Dante DeBlassie",
title = "The Chance of a Long Lifetime for {Brownian} Motion in
a Horn-Shaped Domain",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "14:134--14:139",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1263",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1263",
abstract = "By means of a simple conditioning/comparison argument,
we derive the chance of a long lifetime for Brownian
motion in a horn-shaped domain.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Krikun:2007:CAP,
author = "Maxim Krikun",
title = "Connected allocation to {Poisson} points in {$ \mathbb
{R}^2 $}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "15:140--15:145",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1268",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1268",
abstract = "This note answers one question in [1] concerning the
connected allocation for the Poisson process in $
\mathbb {R}^2 $. The proposed solution makes use of the
Riemann map from the plane minus the minimal spanning
forest of the Poisson point process to the halfplane. A
picture of a numerically simulated example is
included.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Poisson process; Riemann map",
}
@Article{Patie:2007:TSE,
author = "Pierre Patie",
title = "Two-sided exit problem for a Spectrally Negative $
\alpha $-Stable {Ornstein--Uhlenbeck} Process and the
{Wright}'s generalized hypergeometric functions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "16:146--16:160",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1265",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1265",
abstract = "The Laplace transform of the first exit time from a
finite interval by a regular spectrally negative $
\alpha $-stable Ornstein--Uhlenbeck process is provided
in terms of the Wright's generalized hypergeometric
function. The Laplace transform of first passage times
is also derived for some related processes such as the
process killed when it enters the negative half line
and the process conditioned to stay positive. The law
of the maximum of the associated bridges is computed in
terms of the $q$-resolvent density. As a byproduct, we
deduce some interesting analytical properties for some
Wright's generalized hypergeometric functions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "stable Ornstein--Uhlenbeck process; Two-sided exit
time; Wright's generalized hypergeometric functions",
}
@Article{Bojdecki:2007:SEF,
author = "Tomasz Bojdecki and Luis Gorostiza and Anna
Talarczyk",
title = "Some Extensions of Fractional {Brownian} Motion and
Sub-Fractional {Brownian} Motion Related to Particle
Systems",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "17:161--17:172",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1272",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1272",
abstract = "In this paper we study three self-similar, long-range
dependence, Gaussian processes. The first one, with
covariance\par
$$ \int^{s \wedge t}_0 u^a [(t - u)^b + (s - u)^b]d u,
$$
parameters $ a > - 1 $, $ - 1 < b \leq 1 $, $ |b| \leq
1 + a $, corresponds to fractional Brownian motion for
$ a = 0 $, $ - 1 < b < 1 $. The second one, with
covariance\par
$$ (2 - h) \biggl (s^h + t^h - \frac {1}{2}[(s + t)^h
+ |s - t|^h] \biggr), $$
parameter $ 0 < h \leq 4 $, corresponds to
sub-fractional Brownian motion for $ 0 < h < 2 $. The
third one, with covariance\par
$$ - \left (s^2 \log s + t^2 \log t - \frac {1}{2}[(s
+ t)^2 \log (s + t) + (s - t)^2 \log |s - t|] \right),
$$
is related to the second one. These processes come from
occupation time fluctuations of certain particle
systems for some values of the parameters.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "bi-fractional Brownian motion; fractional Brownian
motion; long-range dependence; negative sub-fractional
Brownian motion; particle system; sub-fractional
Brownian motion; weighted fractional Brownian motion",
}
@Article{Funaki:2007:DSL,
author = "Tadahisa Funaki",
title = "Dichotomy in a scaling limit under {Wiener} measure
with density",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "18:173--18:183",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1271",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1271",
abstract = "In general, if the large deviation principle holds for
a sequence of probability measures and its rate
functional admits a unique minimizer, then the measures
asymptotically concentrate in its neighborhood so that
the law of large numbers follows. This paper discusses
the situation that the rate functional has two distinct
minimizers, for a simple model described by the pinned
Wiener measures with certain densities involving a
scaling. We study their asymptotic behavior and
determine to which minimizers they converge based on a
more precise investigation than the large deviation's
level.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Large deviation principle, minimizers, pinned Wiener
measure, scaling limit, concentration",
}
@Article{Bercu:2007:ARE,
author = "Bernard Bercu and W{\l}odek Bryc",
title = "Asymptotic results for empirical measures of weighted
sums of independent random variables",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "19:184--19:199",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1273",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See erratum \cite{Bercu:2022:EAR}.",
URL = "http://ecp.ejpecp.org/article/view/1273",
abstract = "We investigate the asymptotic behavior of weighted
sums of independent standardized random variables with
uniformly bounded third moments. The sequence of
weights is given by a family of rectangular matrices
with uniformly small entries and approximately
orthogonal rows. We prove that the empirical CDF of the
resulting partial sums converges to the normal CDF with
probability one. This result implies almost sure
convergence of empirical periodograms, almost sure
convergence of spectral distribution of circulant and
reverse circulant matrices, and almost sure convergence
of the CDF generated from independent random variables
by independent random orthogonal matrices. In the
special case of trigonometric weights, the speed of the
almost sure convergence is described by a normal
approximation as well as a large deviation principle.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Bose:2007:APR,
author = "Arup Bose and Arnab Sen",
title = "On asymptotic properties of the rank of a special
random adjacency matrix",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "20:200--20:205",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1266",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1266",
abstract = "Consider the matrix $ \Delta_n = ((\ \mathrm {I}(X_i +
X_j > 0))_{i, j = 1, 2, \ldots {}, n} $ where $ \{ X_i
\} $ are i.i.d.\ and their distribution is continuous
and symmetric around $0$. We show that the rank $ r_n$
of this matrix is equal in distribution to $ 2 \sum_{i
= 1}^{n - 1} \mathrm {I}(\xi_i = 1, \xi_{i + 1} = 0) +
\mathrm {I}(\xi_n = 1)$ where $ \xi_i \stackrel
{i.i.d.}{\sim } \text {Ber} (1, 1 / 2).$ As a
consequence $ \sqrt n(r_n / n - 1 / 2)$ is
asymptotically normal with mean zero and variance $ 1 /
4$. We also show that $ n^{-1}r_n$ converges to $ 1 /
2$ almost surely.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Large dimensional random matrix, rank, almost sure
representation, $1$-dependent sequence, almost sure
convergence, convergence in distribution.",
}
@Article{Hutzenthaler:2007:GRS,
author = "Martin Hutzenthaler and Roland Alkemper",
title = "Graphical representation of some duality relations in
stochastic population models",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "21:206--21:220",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1283",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1283",
abstract = "We derive a unified stochastic picture for the duality
of a resampling-selection model with a
branching-coalescing particle process (cf. MR2123250)
and for the self-duality of Feller's branching
diffusion with logistic growth (cf. MR2308333). The two
dual processes are approximated by particle processes
which are forward and backward processes in a graphical
representation. We identify duality relations between
the basic building blocks of the particle processes
which lead to the two dualities mentioned above.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "branching-coalescing particle process; Duality;
Feller's branching diffusion; graphical representation;
resampling-selection model; stochastic population
dynamics",
}
@Article{Liu:2007:SLT,
author = "Wei-Dong Liu and Zheng-Yan Lin",
title = "Some {LIL} type results on the partial sums and
trimmed sums with multidimensional indices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "22:221--22:233",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1286",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1286",
abstract = "Let $ \{ X, X_{{n}}; n \in \mathbb {N}^d \} $ be a
field of i.i.d. random variables indexed by $d$-tuples
of positive integers and let $ S_{{n}} = \sum_{{k} \leq
{n}}X_{{k}}$. We prove some strong limit theorems for $
S_{{n}}$. Also, when $ d \geq 2$ and $ h({n})$
satisfies some conditions, we show that there are no
LIL type results for $ S_{{n}} / \sqrt
{|{n}|h({n})}$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Law of the iterated logarithm; random field; trimmed
sums",
}
@Article{Spruill:2007:ADC,
author = "Marcus Spruill",
title = "Asymptotic Distribution of Coordinates on High
Dimensional Spheres",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "23:234--23:247",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1294",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1294",
abstract = "The coordinates $ x_i $ of a point $ x = (x_1, x_2,
\dots, x_n) $ chosen at random according to a uniform
distribution on the $ \ell_2 (n)$-sphere of radius $
n^{1 / 2}$ have approximately a normal distribution
when $n$ is large. The coordinates $ x_i$ of points
uniformly distributed on the $ \ell_1 (n)$-sphere of
radius $n$ have approximately a double exponential
distribution. In these and all the $ \ell_p(n), 1 \le p
\le \infty, $ convergence of the distribution of
coordinates as the dimension $n$ increases is at the
rate $ \sqrt {n}$ and is described precisely in terms
of weak convergence of a normalized empirical process
to a limiting Gaussian process, the sum of a Brownian
bridge and a simple normal process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "dependent arrays; empiric distribution; isoperimetry;
micro-canonical ensemble; Minkowski area",
}
@Article{Rao:2007:MFR,
author = "N. Raj Rao and Roland Speicher",
title = "Multiplication of free random variables and the
{$S$}-transform: the case of vanishing mean",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "24:248--24:258",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1274",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1274",
abstract = "This note extends Voiculescu's {\em S\/}-transform
based analytical machinery for free multiplicative
convolution to the case where the mean of the
probability measures vanishes. We show that with the
right interpretation of the {\em S\/}-transform in the
case of vanishing mean, the usual formula makes
perfectly good sense.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "free multiplicative convolution; Random matrices, free
probability",
}
@Article{Jost:2007:NET,
author = "C{\'e}line Jost",
title = "A note on ergodic transformations of self-similar
{Volterra} {Gaussian} processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "25:259--25:266",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1298",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1298",
abstract = "We derive a class of ergodic transformation of
self-similar Gaussian processes that are Volterra, i.e.
of type $ X_t = \int^t_0 z_X(t, s)d W_s $, $ t \in [0,
\infty) $, where $ z_X $ is a deterministic kernel and
$W$ is a standard Brownian motion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Ergodic transformation; Fractional Brownian motion;
Self-similar process; Volterra Gaussian process",
}
@Article{Yang:2007:TMP,
author = "Ming Yang",
title = "On a theorem in multi-parameter potential theory",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "26:267--26:275",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1293",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1293",
abstract = "We prove that the expected Lebesgue measure of the
range of an additive L{\'e}vy process is positive if
and only if the product $ \Re ([1 + \Psi_1 (\xi)]^{-1})
\ldots {} \Re ([1 + \Psi_N(\xi)]^{-1}) $ is integrable.
This was previously proved by Khoshnevisan, Xiao and
Zhong [1] under a sector condition.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Additive L{\'e}vy processes, Hausdorff dimension,
multiple points.",
}
@Article{Tamas:2007:DDN,
author = "M{\'o}ri Tam{\'a}s",
title = "Degree distribution nearby the origin of a
preferential attachment graph",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "27:276--27:282",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1299",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1299",
abstract = "In a 2-parameter scale free model of random graphs it
is shown that the asymptotic degree distribution is the
same in the neighbourhood of every vertex. This degree
distribution is still a power law with characteristic
exponent 2, but this exponent is different from the one
observed in the whole graph.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "degree distribution; martingale; Scale free graphs",
}
@Article{Arguin:2007:DCP,
author = "Louis-Pierre Arguin",
title = "A dynamical characterization of {Poisson--Dirichlet}
distributions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "28:283--28:290",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1300",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1300",
abstract = "We show that a slight modification of a theorem of
Ruzmaikina and Aizenman on competing particle systems
on the real line leads to a characterization of
Poisson--Dirichlet distributions $ P D(\alpha, 0) $.
Precisely, let $ \xi $ be a proper random
mass-partition i.e. a random sequence $ (\xi_i, i \in
N) $ such that $ \xi_1 \geq \xi_2 \geq \dots \geq 0 $
and $ \sum_i \xi_i = 1 $ a.s. Consider $ \{ W_i \}_{i
\in N} $, an iid sequence of random positive numbers
whose distribution is absolutely continuous with
respect to the Lebesgue measure and $ E[W^\lambda] <
\infty $ for all $ \lambda \in R $. It is shown that,
if the law of $ \xi $ is invariant under the random
reshuffling\par
$$ (\xi_i, i \in N) \to \left (\frac {\xi_i
W_i}{\sum_j \xi_jW_j }, i \in N \right) $$
where the weights are reordered after evolution, then
it must be a mixture of Poisson--Dirichlet
distributions $ P D(\alpha, 0), \alpha \in (0, 1) $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Point processes, Poisson--Dirichlet distributions",
}
@Article{Baldi:2007:CIG,
author = "Paolo Baldi and Domenico Marinucci and Veeravalli
Varadarajan",
title = "On the characterization of isotropic {Gaussian} fields
on homogeneous spaces of compact groups",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "29:291--29:302",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1316",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1316",
abstract = "Let $T$ be a random field weakly invariant under the
action of a compact group $G$. We give conditions
ensuring that independence of the random Fourier
coefficients is equivalent to Gaussianity. As a
consequence, in general it is not possible to simulate
a non-Gaussian invariant random field through its
Fourier expansion using independent coefficients",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "isotropic Random Fields, Fourier expansions,
Characterization of Gaussian Random Fields",
}
@Article{Berard:2007:CLT,
author = "Jean Berard and Alejandro Ramirez",
title = "{Central Limit Theorem} For The Excited Random Walk In
Dimension $ d \geq 2 $",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "30:303--30:314",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1317",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1317",
abstract = "We prove that a law of large numbers and a central
limit theorem hold for the excited random walk model in
every dimension $ d \geq 2 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Excited random walk, Regeneration techniques",
}
@Article{Meckes:2007:SNR,
author = "Mark Meckes",
title = "On the spectral norm of a random {Toeplitz} matrix",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "31:315--31:325",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1313",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1313",
abstract = "Suppose that $ T_n $ is a Toeplitz matrix whose
entries come from a sequence of independent but not
necessarily identically distributed random variables
with mean zero. Under some additional tail conditions,
we show that the spectral norm of $ T_n $ is of the
order $ \sqrt {n \log n} $. The same result holds for
random Hankel matrices as well as other variants of
random Toeplitz matrices which have been studied in the
literature.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "random Toeplitz matrix, random Hankel matrix, spectral
norm",
}
@Article{Zerner:2007:ZOL,
author = "Martin Zerner",
title = "The zero-one law for planar random walks in i.i.d.
random environments revisited",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "32:326--32:335",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1314",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1314",
abstract = "In this note we present a simplified proof of the
zero-one law by Merkl and Zerner (2001) for directional
transience of random walks in i.i.d. random
environments (RWRE) on the square lattice. Also, we
indicate how to construct a two-dimensional
counterexample in a non-uniformly elliptic and
stationary environment which has better ergodic
properties than the example given by Merkl and
Zerner.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random environment, random walk, RWRE, transience,
zero-one law",
}
@Article{Andrieu:2007:EAM,
author = "Christophe Andrieu and Yves Atchade",
title = "On the efficiency of adaptive {MCMC} algorithms",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "33:336--33:349",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1320",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1320",
abstract = "We study a class of adaptive Markov Chain Monte Carlo
(MCMC) processes which aim at behaving as an
``optimal'' target process via a learning procedure. We
show, under appropriate conditions, that the adaptive
MCMC chain and the ``optimal'' (nonadaptive) MCMC
process share many asymptotic properties. The special
case of adaptive MCMC algorithms governed by stochastic
approximation is considered in details and we apply our
results to the adaptive Metropolis algorithm of
[Haario, Saksman, Tamminen].",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Peccati:2007:GAM,
author = "Giovanni Peccati",
title = "{Gaussian} Approximations of Multiple Integrals",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "34:350--34:364",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1322",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1322",
abstract = "Fix $ k \geq 1 $, and let $ I(l), l \geq 1 $, be a
sequence of $k$-dimensional vectors of multiple
Wiener-It{\^o} integrals with respect to a general
Gaussian process. We establish necessary and sufficient
conditions to have that, as $ l \to \infty $, the law
of $ I(l)$ is asymptotically close (for example, in the
sense of Prokhorov's distance) to the law of a
$k$-dimensional Gaussian vector having the same
covariance matrix as $ I(l)$. The main feature of our
results is that they require minimal assumptions
(basically, boundedness of variances) on the asymptotic
behaviour of the variances and covariances of the
elements of $ I(l)$. In particular, we will not assume
that the covariance matrix of $ I(l)$ is convergent.
This generalizes the results proved in Nualart and
Peccati (2005), Peccati and Tudor (2005) and Nualart
and Ortiz-Latorre (2007). As shown in Marinucci and
Peccati (2007b), the criteria established in this paper
are crucial in the study of the high-frequency
behaviour of stationary fields defined on homogeneous
spaces.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Gaussian processes; Malliavin calculus; Multiple
stochastic integrals; Non-central limit theorems; Weak
convergence",
}
@Article{Benjamini:2007:MAP,
author = "Itai Benjamini and Ariel Yadin and Ofer Zeitouni",
title = "Maximal Arithmetic Progressions in Random Subsets",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "35:365--35:376",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1321",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See erratum \cite{Benjamini:2012:EMA}.",
URL = "http://ecp.ejpecp.org/article/view/1321",
abstract = "Let $ U(N) $ denote the maximal length of arithmetic
progressions in a random uniform subset of $ \{ 0, 1
\}^N $. By an application of the Chen-Stein method, we
show that $ U(N) - 2 \log (N) / \log (2) $ converges in
law to an extreme type (asymmetric) distribution. The
same result holds for the maximal length $ W(N) $ of
arithmetic progressions (mod $N$). When considered in
the natural way on a common probability space, we
observe that $ U(N) / \log (N)$ converges almost surely
to $ 2 / \log (2)$, while $ W(N) / \log (N)$ does not
converge almost surely (and in particular, $ \limsup
W(N) / \log (N)$ is at least $ 3 / \log (2)$).\par
\url{https://doi.org/10.1214/ECP.v17-2014} {\bf An
Erratum is available in ECP volume {\bf 17} paper
number 18.}",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "arithmetic progression; Chen-Stein method; dependency
graph; extreme type limit distribution; random subset",
}
@Article{Montenegro:2007:SEV,
author = "Ravi Montenegro",
title = "Sharp edge, vertex, and mixed {Cheeger} type
inequalities for finite {Markov} kernels",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "36:377--36:389",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1269",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1269",
abstract = "We show how the evolving set methodology of Morris and
Peres can be used to show Cheeger inequalities for
bounding the spectral gap of a finite Markov kernel.
This leads to sharp versions of several previous
Cheeger inequalities, including ones involving
edge-expansion, vertex-expansion, and mixtures of both.
A bound on the smallest eigenvalue also follows.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Markov chain, evolving sets, Cheeger inequality,
eigenvalues",
}
@Article{Darses:2007:DPC,
author = "S{\'e}bastien Darses and Ivan Nourdin",
title = "Dynamical properties and characterization of gradient
drift diffusions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "37:390--37:400",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1324",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1324",
abstract = "We study the dynamical properties of the Brownian
diffusions having $ \sigma \, {\rm Id} $ as diffusion
coefficient matrix and $ b = \nabla U $ as drift
vector. We characterize this class through the equality
$ D^2_+= D^2_- $, where $ D_+ $ (resp. $ D_-$) denotes
the forward (resp. backward) stochastic derivative of
Nelson's type. Our proof is based on a remarkable
identity for $ D_+^2 - D_-^2$ and on the use of the
martingale problem.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Gradient drift diffusion; Kolmogorov theorem;
Martingale problem; Nelson stochastic derivatives;
Reversible diffusion; Stationary diffusion; Time
reversal",
}
@Article{Panchenko:2007:NTP,
author = "Dmitriy Panchenko",
title = "A note on {Talagrand}'s positivity principle",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "38:401--38:410",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1326",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1326",
abstract = "Talagrand's positivity principle states that one can
slightly perturb a Hamiltonian in the
Sherrington-Kirkpatrick model in such a way that the
overlap of two configurations under the perturbed
Gibbs' measure will become typically nonnegative. In
this note we observe that abstracting from the setting
of the SK model only improves the result and does not
require any modifications in Talagrand's argument. In
this version, for example, positivity principle
immediately applies to the setting of replica symmetry
breaking interpolation. Also, abstracting from the SK
model improves the conditions in the Ghirlanda-Guerra
identities and as a consequence results in a
perturbation of smaller order necessary to ensure
positivity of the overlap.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Talagrand's positivity principle, Ghirlanda-Guerra
identities",
}
@Article{vandenBerg:2007:SPI,
author = "Jacob van den Berg and Antal Jarai and Balint
Vagvolgyi",
title = "The size of a pond in 2D invasion percolation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "39:411--39:420",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1327",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1327",
abstract = "We consider invasion percolation on the square
lattice. van den Berg, Peres, Sidoravicius and Vares
have proved that the probability that the radius of a
so-called pond is larger than n, differs at most a
factor of order log n from the probability that in
critical Bernoulli percolation the radius of an open
cluster is larger than n. We show that these two
probabilities are, in fact, of the same order.
Moreover, we prove an analogous result for the volume
of a pond.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "critical percolation; invasion percolation; pond",
}
@Article{Cox:2007:SRT,
author = "Sonja Cox and Mark Veraar",
title = "Some remarks on tangent martingale difference
sequences in {$ L^1 $}-spaces",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "40:421--40:433",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1328",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1328",
abstract = "Let $X$ be a Banach space. Suppose that for all $ p
\in (1, \infty)$ a constant $ C_{p, X}$ depending only
on $X$ and $p$ exists such that for any two $X$-valued
martingales $f$ and $g$ with tangent martingale
difference sequences one has\par
$$ \mathbb {E} \| f \|^p \leq C_{p, X} \mathbb {E} \|
g \|^p \qquad (*). $$
This property is equivalent to the UMD condition. In
fact, it is still equivalent to the UMD condition if in
addition one demands that either $f$ or $g$ satisfy the
so-called (CI) condition. However, for some
applications it suffices to assume that $ (*)$ holds
whenever $g$ satisfies the (CI) condition. We show that
the class of Banach spaces for which $ (*)$ holds
whenever only $g$ satisfies the (CI) condition is more
general than the class of UMD spaces, in particular it
includes the space $ L^1$. We state several problems
related to $ (*)$ and other decoupling inequalities.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Davis decomposition; decoupling inequalities;
martingale difference sequences; tangent sequences; UMD
Banach spaces",
}
@Article{Van:2007:SLL,
author = "Thanh Le Van",
title = "On the strong law of large numbers for $d$-dimensional
arrays of random variables",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "41:434--41:441",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1331",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1331",
abstract = "In this paper, we provide a necessary and sufficient
condition for general $d$-dimensional arrays of random
variables to satisfy strong law of large numbers. Then,
we apply the result to obtain some strong laws of large
numbers for $d$-dimensional arrays of blockwise
independent and blockwise orthogonal random
variables.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Strong law of large number, almost sure convergence,
$d$-dimensional arrays of random variables",
}
@Article{DaPrato:2007:MKP,
author = "Giuseppe {Da Prato} and Arnaud Debussche and Luciano
Tubaro",
title = "A modified {Kardar--Parisi--Zhang} model",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "42:442--42:453",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1333",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1333",
abstract = "A one dimensional stochastic differential equation of
the form
$$ d X = A X d t + \frac 12 ( - A)^{- \alpha }
\partial_\xi [(( - A)^{- \alpha }X)^2]d t +
\partial_\xi d W(t), \qquad X(0) = x $$
is considered, where $ A = \frac 12 \partial^2_\xi $.
The equation is equipped with periodic boundary
conditions. When $ \alpha = 0 $ this equation arises in
the Kardar--Parisi--Zhang model. For $ \alpha \ne 0 $,
this equation conserves two important properties of the
Kardar--Parisi--Zhang model: it contains a quadratic
nonlinear term and has an explicit invariant measure
which is Gaussian. However, it is not as singular and
using renormalization and a fixed point result we prove
existence and uniqueness of a strong solution provided
$ \alpha > \frac 18 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "invariant measure; Stochastic partial differential
equations; white noise; Wick product",
}
@Article{Haggstrom:2007:VCM,
author = "Olle H{\"a}ggstr{\"om} and Jeffrey Rosenthal",
title = "On Variance Conditions for {Markov} Chain {CLTs}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "43:454--43:464",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1336",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1336",
abstract = "Central limit theorems for Markov chains are
considered, and in particular the relationships between
various expressions for asymptotic variance known from
the literature. These turn out to be equal under fairly
general conditions, although not always. We also
investigate the existence of CLTs, and pose some open
problems.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Oraby:2007:SLH,
author = "Tamer Oraby",
title = "The spectral laws of {Hermitian} block-matrices with
large random blocks",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "12",
pages = "44:465--44:476",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v12-1335",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1335",
abstract = "We are going to study the limiting spectral measure of
fixed dimensional Hermitian block-matrices with large
dimensional Wigner blocks. We are going also to
identify the limiting spectral measure when the
Hermitian block-structure is Circulant. Using the
limiting spectral measure of a Hermitian Circulant
block-matrix we will show that the spectral measure of
a Wigner matrix with k-weakly dependent entries need
not to be the semicircle law in the limit.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random matrices",
}
@Article{Fierro:2007:SSA,
author = "Raul Fierro and Soledad Torres",
title = "A stochastic scheme of approximation for ordinary
differential equations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "1:1--1:9",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1341",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1341",
abstract = "In this note we provide a stochastic method for
approximating solutions of ordinary differential
equations. To this end, a stochastic variant of the
Euler scheme is given by means of Markov chains. For an
ordinary differential equation, these approximations
are shown to satisfy a Large Number Law, and a Central
Limit Theorem for the corresponding fluctuations about
the solution of the differential equation is proven.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Central limit theorem; Convergence in law; Numerical
Scheme",
}
@Article{Feyel:2007:NCS,
author = "Denis Feyel and Arnaud {de La Pradelle} and Gabriel
Mokobodzki",
title = "A non-commutative sewing lemma",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "3:24--3:34",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1345",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1345",
abstract = "A non-commutative version of the sewing lemma is
proved, with some applications",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Curvilinear Integrals, Rough Paths, Stochastic
Integrals",
}
@Article{Wu:2008:LDP,
author = "Liming Wu and Nian Yao",
title = "Large deviation principles for {Markov} processes via
{Phi--Sobolev} inequalities",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "2:10--2:23",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1342",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1342",
abstract = "Via Phi-Sobolev inequalities, we give some sharp
integrability conditions on $F$ for the large deviation
principle of the empirical mean $ \frac
{1}{T}{\int_0^T{F(X_s)}ds}$ for large time $T$, where
$F$ is unbounded with values in some separable Banach
space. Several examples are provided.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "functional inequalities; large deviations; Orlicz
space",
}
@Article{Rossignol:2008:TPP,
author = "Rapha{\"e}l Rossignol",
title = "Threshold phenomena on product spaces: BKKKL revisited
(once more)",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "4:35--4:44",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1344",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1344",
abstract = "We revisit the work of Bourgain et al. (1992) -
referred to as {"BKKKL"} in the title - about
influences on Boolean functions in order to give a
precise statement of threshold phenomenon on the
product space $ \{ 1, \ldots {}, r \}^N $, generalizing
one of the main results of Talagrand (1994).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Threshold phenomenon, approximate zero-one law,
influences.",
}
@Article{LePrince:2008:RBD,
author = "Vincent {Le Prince}",
title = "A relation between dimension of the harmonic measure,
entropy and drift for a random walk on a hyperbolic
space",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "5:45--5:53",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1350",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1350",
abstract = "We establish in this paper an exact formula which
links the dimension of the harmonic measure, the
asymptotic entropy and the rate of escape for a random
walk on a discrete subgroup of the isometry group of a
Gromov hyperbolic space. This completes a result
obtained by the author in a previous paper, where only
an upper bound for the dimension was proved.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "drift; entropy; harmonic measure; hyperbolic space;
Random walk",
}
@Article{vanZanten:2008:REG,
author = "Harry van Zanten",
title = "A remark on the equivalence of {Gaussian} processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "6:54--6:59",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1348",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1348",
abstract = "In this note we extend a classical equivalence result
for Gaussian stationary processes to the more general
setting of Gaussian processes with stationary
increments. This will allow us to apply it in the
setting of aggregated independent fractional Brownian
motions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "equivalence of laws, spectral method; Gaussian
processes with stationary increments",
}
@Article{Bakry:2008:SPP,
author = "Dominique Bakry and Franck Barthe and Patrick Cattiaux
and Arnaud Guillin",
title = "A simple proof of the {Poincar{\'e}} inequality for a
large class of probability measures",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "7:60--7:66",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1352",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1352",
abstract = "Abstract. We give a simple and direct proof of the
existence of a spectral gap under some Lyapunov type
condition which is satisfied in particular by
log-concave probability measures on $ \mathbb {R}^n $.
The proof is based on arguments introduced in Bakry and
al, but for the sake of completeness, all details are
provided.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Lyapunov functions, Poincar{\'e} inequality,
log-concave measure",
}
@Article{Lawi:2008:HLP,
author = "Stephan Lawi",
title = "{Hermite} and {Laguerre} Polynomials and Matrix-Valued
Stochastic Processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "8:67--8:84",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1353",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1353",
abstract = "We extend to matrix-valued stochastic processes, some
well-known relations between real-valued diffusions and
classical orthogonal polynomials, along with some
recent results about L{\'e}vy processes and martingale
polynomials. In particular, joint semigroup densities
of the eigenvalue processes of the generalized
matrix-valued Ornstein--Uhlenbeck and squared
Ornstein--Uhlenbeck processes are respectively
expressed by means of the Hermite and Laguerre
polynomials of matrix arguments. These polynomials also
define martingales for the Brownian matrix and the
generalized Gamma process. As an application, we derive
a chaotic representation property for the eigenvalue
process of the Brownian matrix.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian matrices, Wishart processes, Hermite
polynomials, Laguerre polynomials, martingale
polynomials, chaos representation property",
}
@Article{Bednorz:2008:RPC,
author = "Witold Bednorz and Krzysztof Latuszynski and Rafal
Latala",
title = "A Regeneration Proof of the {Central Limit Theorem}
for Uniformly Ergodic {Markov} Chains",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "9:85--9:98",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1354",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1354",
abstract = "Central limit theorems for functionals of general
state space Markov chains are of crucial importance in
sensible implementation of Markov chain Monte Carlo
algorithms as well as of vital theoretical interest.
Different approaches to proving this type of results
under diverse assumptions led to a large variety of CLT
versions. However due to the recent development of the
regeneration theory of Markov chains, many classical
CLTs can be reproved using this intuitive probabilistic
approach, avoiding technicalities of original proofs.
In this paper we provide a characterization of CLTs for
ergodic Markov chains via regeneration and then use the
result to solve the open problem posed in [Roberts \&
Rosenthal 2005]. We then discuss the difference between
one-step and multiple-step small set condition.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Markov chains, central limit theorems, regeneration,
ergodicity, uniform ergodicity, Harris recurrence",
}
@Article{McVinish:2008:OPE,
author = "Ross McVinish",
title = "Optimising prediction error among completely monotone
covariance sequences",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "11:113--11:120",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1355",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1355",
abstract = "We provide a characterisation of Gaussian time series
which optimise the one-step prediction error subject to
the covariance sequence being completely monotone with
the first {\em m\/} covariances specified.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "aggregation; maximum entropy; moment space",
}
@Article{Gao:2008:EEM,
author = "Fuchang Gao",
title = "Entropy Estimate for $k$-Monotone Functions via Small
Ball Probability of Integrated {Brownian} Motions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "12:121--12:130",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1357",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1357",
abstract = "Metric entropy of the class of probability
distribution functions on $ [0, 1] $ with a
$k$-monotone density is studied through its connection
with the small ball probability of $k$-times integrated
Brownian motions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "metric entropy, $k$-monotone function, small ball
probability, $k$-times integrated Brownian motion",
}
@Article{Rolla:2008:LPP,
author = "Leonardo Rolla and Augusto Teixeira",
title = "Last Passage Percolation in Macroscopically
Inhomogeneous Media",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "13:131--13:139",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1287",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1287",
abstract = "In this note we investigate the last passage
percolation model in the presence of macroscopic
inhomogeneity. We analyze how this affects the scaling
limit of the passage time, leading to a variational
problem that provides an ODE for the deterministic
limiting shape of the maximal path. We obtain a
sufficient analytical condition for uniqueness of the
solution for the variational problem. Consequences for
the totally asymmetric simple exclusion process are
discussed.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "inhomogeneous media; last passage percolation; scaling
limit; tasep; variational problem",
}
@Article{Windisch:2008:RWD,
author = "David Windisch",
title = "Random walk on a discrete torus and random
interlacements",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "14:140--14:150",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1359",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1359",
abstract = "We investigate the relation between the local picture
left by the trajectory of a simple random walk on the
torus $ ({\mathbb Z} / N{\mathbb Z})^d $, $ d \geq 3 $,
until $ u N^d $ time steps, $ u > 0 $, and the model of
random interlacements recently introduced by Sznitman.
In particular, we show that for large $N$, the joint
distribution of the local pictures in the neighborhoods
of finitely many distant points left by the walk up to
time $ u N^d$ converges to independent copies of the
random interlacement at level $u$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "random interlacements; Random walk",
}
@Article{Maas:2008:COF,
author = "Jan Maas and Jan Neerven",
title = "A {Clark--Ocone} formula in {UMD} {Banach} spaces",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "15:151--15:164",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1361",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1361",
abstract = "Let $H$ be a separable real Hilbert space and let $
\mathbb {F} = (\mathscr {F}_t)_{t \in [0, T]}$ be the
augmented filtration generated by an $H$-cylindrical
Brownian motion $ (W_H(t))_{t \in [0, T]}$ on a
probability space $ (\Omega, \mathscr {F}, \mathbb
{P})$. We prove that if $E$ is a UMD Banach space, $ 1
\le p < \infty $, and $ F \in \mathbb {D}^{1,
p}(\Omega; E)$ is $ \mathscr {F}_T$-measurable,
then\par
$$ F = \mathbb {E} (F) + \int_0^T P_{\mathbb {F}} (D
F) \, d W_H, $$
where $D$ is the Malliavin derivative of $F$ and $
P_{\mathbb {F}}$ is the projection onto the $ {\mathbb
{F}}$-adapted elements in a suitable Banach space of $
L^p$-stochastically integrable $ \mathscr {L}(H,
E)$-valued processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Clark-Ocone formula, Malliavin calculus",
}
@Article{Sturm:2008:TVM,
author = "Anja Sturm and Jan Swart",
title = "Tightness of voter model interfaces",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "16:165--16:174",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1360",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1360",
abstract = "Consider a long-range, one-dimensional voter model
started with all zeroes on the negative integers and
all ones on the positive integers. If the process
obtained by identifying states that are translations of
each other is positively recurrent, then it is said
that the voter model exhibits interface tightness. In
1995, Cox and Durrett proved that one-dimensional voter
models exhibit interface tightness if their infection
rates have a finite third moment. Recently, Belhaouari,
Mountford, and Valle have improved this by showing that
a finite second moment suffices. The present paper
gives a new short proof of this fact. We also prove
interface tightness for a long range swapping voter
model, which has a mixture of long range voter model
and exclusion process dynamics.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "exclusion process.; interface tightness; Long range
voter model; swapping voter model",
}
@Article{Latala:2008:BBP,
author = "Rafal Latala",
title = "On the boundedness of {Bernoulli} processes over thin
sets",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "17:175--17:186",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1362",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1362",
abstract = "We show that the Bernoulli conjecture holds for sets
with small one-dimensional projections, i.e. any
bounded Bernoulli process indexed by such set may be
represented as a sum of a uniformly bounded process and
a process dominated by a bounded Gaussian process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bernoulli process, Bernoulli conjecture, partitioning
scheme, majorizing measure",
}
@Article{Gnedin:2008:CRP,
author = "Alexander Gnedin",
title = "Corners and Records of the {Poisson} Process in
Quadrant",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "18:187--18:193",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1351",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1351",
abstract = "The scale-invariant spacings lemma due to Arratia,
Barbour and Tavar{\'e} establishes the distributional
identity of a self-similar Poisson process and the set
of spacings between the points of this process. In this
note we connect this result with properties of a
certain set of extreme points of the unit Poisson
process in the positive quadrant",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "$k$-records, $k$-corners, self-similar Poisson
process, Ignatov's theorem",
}
@Article{Pal:2008:SB,
author = "Soumik Pal",
title = "Symmetrization of {Bernoulli}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "19:194--19:197",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1364",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1364",
abstract = "We show that an asymmetric Bernoulli random variable
is symmetry resistant in the sense that any independent
random variable, which when added to it produces a
symmetric sum, must have a variance at least as much as
itself. The main instrument is to use Skorokhod
embedding to transfer the discrete problem to the realm
of stochastic calculus.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Symmetrization, symmetry resistant, Skorokhod
embedding",
}
@Article{Eisenbaum:2008:PGG,
author = "Nathalie Eisenbaum and Andreas Kyprianou",
title = "On the parabolic generator of a general
one-dimensional {L{\'e}vy} process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "20:198--20:209",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1366",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1366",
abstract = "The purpose of this note is twofold. Firstly to
complete a recent accumulation of results concerning
extended version of Ito's formula for any one
dimensional L{\'e}vy processes, $X$. Secondly, we use
the latter to characterise the parabolic generator of
$X$,
$$ {\bf A} := \left \{ (f, g) : f(X_\cdot, \cdot) -
\int_0^\cdot g(X_s, s)d s \text { is a local
martingale} \right \} . $$
We also establish a necessary condition for a pair of
functions to be in the domain of the parabolic
generator when $X$ has a Gaussian component.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stochastic calculus , local time-space, It{\^o}
formula, parabolic generator.",
}
@Article{Makhnin:2008:FPE,
author = "Oleg Makhnin",
title = "Filtering and parameter estimation for a jump
stochastic process with discrete observations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "21:210--21:224",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1363",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1363",
abstract = "A compound Poisson process is considered. We estimate
the current position of the stochastic process based on
past discrete-time observations (non-linear discrete
filtering problem) in Bayesian setting. We obtain
bounds for the asymptotic rate of the expected square
error of the filter when observations become frequent.
The bounds depend linearly on jump intensity. Also,
estimation of process' parameters is addressed.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Comman:2008:SWT,
author = "Henri Comman",
title = "{Stone--Weierstrass} type theorems for large
deviations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "22:225--22:240",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1370",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1370",
abstract = "We give a general version of Bryc's theorem valid on
any topological space and with any algebra $ \mathcal
{A} $ of real-valued continuous functions separating
the points, or any well-separating class. In absence of
exponential tightness, and when the underlying space is
locally compact regular and $ \mathcal {A} $
constituted by functions vanishing at infinity, we give
a sufficient condition on the functional $ \Lambda
(\cdot)_{\mid \mathcal {A}} $ to get large deviations
with not necessarily tight rate function. We obtain the
general variational form of any rate function on a
completely regular space; when either exponential
tightness holds or the space is locally compact
Hausdorff, we get it in terms of any algebra as above.
Prohorov-type theorems are generalized to any space,
and when it is locally compact regular the exponential
tightness can be replaced by a (strictly weaker)
condition on $ \Lambda (\cdot)_{\mid \mathcal {A}} $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Large deviations, rate function, Bryc's theorem",
}
@Article{Panchenko:2008:DPF,
author = "Dmitry Panchenko",
title = "On differentiability of the {Parisi} formula",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "23:241--23:247",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1365",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1365",
abstract = "It was proved by Michel Talagrand in [10] that the
Parisi formula for the free energy in the
Sherrington-Kirkpatrick model is differentiable with
respect to inverse temperature parameter. We present a
simpler proof of this result by using approximate
solutions in the Parisi formula and give one example of
application of the differentiability to prove non
self-averaging of the overlap outside of the replica
symmetric region.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Sherrington-Kirkpatrick model, Parisi formula.",
}
@Article{Miermont:2008:SSL,
author = "Gr{\'e}gory Miermont",
title = "On the sphericity of scaling limits of random planar
quadrangulations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "24:248--24:257",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1368",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1368",
abstract = "We give a new proof of a theorem by Le Gall and
Paulin, showing that scaling limits of random planar
quadrangulations are homeomorphic to the 2-sphere. The
main geometric tool is a reinforcement of the notion of
Gromov-Hausdorff convergence, called 1-regular
convergence, that preserves topological properties of
metric surfaces.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random planar maps, scaling limits, Gromov-Hausdorff
convergence, spherical topology",
}
@Article{Wastlund:2008:RMP,
author = "Johan W{\"a}stlund",
title = "Random matching problems on the complete graph",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "25:258--25:265",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1372",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1372",
abstract = "The edges of the complete graph on $n$ vertices are
assigned independent exponentially distributed costs. A
$k$-matching is a set of $k$ edges of which no two have
a vertex in common. We obtain explicit bounds on the
expected value of the minimum total cost $ C_{k, n}$ of
a $k$-matching. In particular we prove that if $ n = 2
k$ then $ \pi^2 / 12 < E C_{k, n} < \pi^2 / 12 + \log n
/ n$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Minimum matching, exponential, expectation, mean
field, network.",
}
@Article{Bobkov:2008:NDM,
author = "Sergey Bobkov",
title = "A note on the distributions of the maximum of linear
{Bernoulli} processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "26:266--26:271",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1375",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1375",
abstract = "We give a characterization of the family of all
probability measures on the extended line $ ( - \infty,
+ \infty] $, which may be obtained as the distribution
of the maximum of some linear Bernoulli process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "distribution of the maximum; Linear Bernoulli
processes",
}
@Article{Huss:2008:IDL,
author = "Wilfried Huss",
title = "Internal Diffusion-Limited Aggregation on non-amenable
graphs",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "27:272--27:279",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1374",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1374",
abstract = "The stochastic growth model Internal Diffusion Limited
Aggregation was defined in 1991 by Diaconis and Fulton.
Several shape results are known when the underlying
state space is the d-dimensional lattice, or a discrete
group with exponential growth. We prove an extension of
the shape result of Blachere and Brofferio for Internal
Diffusion Limited Aggregation on a wide class of Markov
chains on non-amenable graphs.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "interacting particle systems; random walks on graphs",
}
@Article{Peche:2008:LBS,
author = "Sandrine Peche and Alexander Soshnikov",
title = "On the lower bound of the spectral norm of symmetric
random matrices with independent entries",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "28:280--28:290",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1376",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1376",
abstract = "We show that the spectral radius of an $ N \times N $
random symmetric matrix with i.i.d. bounded centered
but non-symmetrically distributed entries is bounded
from below by $ 2 \sigma - o(N^{-6 / 11 + \varepsilon
}), $ where $ \sigma^2 $ is the variance of the matrix
entries and $ \varepsilon $ is an arbitrary small
positive number. Combining with our previous result
from [7], this proves that for any $ \varepsilon > 0, \
$ one has $ \| A_N \| = 2 \sigma + o(N^{-6 / 11 +
\varepsilon }) $ with probability going to $1$ as $ N
\to \infty $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Wigner random matrices, spectral norm",
}
@Article{Holmes:2008:EIA,
author = "Mark Holmes and Remco van der Hofstad and Gordon
Slade",
title = "An extension of the inductive approach to the lace
expansion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "29:291--29:301",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1377",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1377",
abstract = "We extend the inductive approach to the lace
expansion, previously developed to study models with
critical dimension 4, to be applicable more generally.
In particular, the result of this note has recently
been used to prove Gaussian asymptotic behaviour for
the Fourier transform of the two-point function for
sufficiently spread-out lattice trees in dimensions $ d
> 8 $, and it is potentially also applicable to
percolation in dimensions $ d > 6 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "induction; Lace expansion; lattice trees;
percolation",
}
@Article{Kabluchko:2008:ECR,
author = "Zakhar Kabluchko and Axel Munk",
title = "Exact Convergence Rate for the Maximum of Standardized
{Gaussian} Increments",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "30:302--30:310",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1380",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1380",
abstract = "We prove an almost sure limit theorem on the exact
convergence rate of the maximum of standardized
Gaussian random walk increments. This gives a more
precise version of Shao's theorem ({\em Shao, Q.-M.,
1995. On a conjecture of R{\'e}v{\'e}sz. Proc. Amer.
Math. Soc. {\bf 123}, 575--582}) in the Gaussian
case.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "standardized increments, Gaussian random walk,
multiscale statistic, L{\'e}vy's continuity modulus,
integral test, almost sure limit theorem",
}
@Article{Morris:2008:SGI,
author = "Ben Morris",
title = "Spectral gap for the interchange process in a box",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "31:311--31:318",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1381",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1381",
abstract = "We show that the spectral gap for the interchange
process (and the symmetric exclusion process) in a
$d$-dimensional box of side length $L$ is asymptotic to
$ \pi^2 / L^2$. This gives more evidence in favor of
Aldous's conjecture that in any graph the spectral gap
for the interchange process is the same as the spectral
gap for a corresponding continuous-time random walk.
Our proof uses a technique that is similar to that used
by Handjani and Jungreis, who proved that Aldous's
conjecture holds when the graph is a tree.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "spectral gap, interchange process",
}
@Article{Vovk:2008:CTT,
author = "Vladimir Vovk",
title = "Continuous-time trading and the emergence of
volatility",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "32:319--32:324",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1383",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1383",
abstract = "This note continues investigation of randomness-type
properties emerging in idealized financial markets with
continuous price processes. It is shown, without making
any probabilistic assumptions, that the strong
variation exponent of non-constant price processes has
to be 2, as in the case of continuous martingales.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "continuous time; game-theoretic probability; strong
variation exponent",
}
@Article{Song:2008:RBS,
author = "Renming Song and Zoran Vondracek",
title = "On the relationship between subordinate killed and
killed subordinate processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "33:325--33:336",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1388",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1388",
abstract = "We study the precise relationship between the
subordinate killed and killed subordinate processes in
the case of an underlying Hunt process, and show that,
under minimal conditions, the former is a subprocess of
the latter obtained by killing at a terminal time.
Moreover, we also show that the killed subordinate
process can be obtained by resurrecting the subordinate
killed one at most countably many times.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Markov process, subordination, killing, resurrection",
}
@Article{Guillotin-Plantard:2008:FLT,
author = "Nadine Guillotin-Plantard and Arnaud {Le Ny}",
title = "A functional limit theorem for a 2d-random walk with
dependent marginals",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "34:337--34:351",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1386",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1386",
abstract = "We prove a non-standard functional limit theorem for a
two dimensional simple random walk on some randomly
oriented lattices. This random walk, already known to
be transient, has different horizontal and vertical
fluctuations leading to different normalizations in the
functional limit theorem, with a non-Gaussian
horizontal behavior. We also prove that the horizontal
and vertical components are not asymptotically
independent.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random walks, random environments, random sceneries",
}
@Article{Gobet:2008:SEC,
author = "Emmanuel Gobet and C{\'e}line Labart",
title = "Sharp estimates for the convergence of the density of
the {Euler} scheme in small time",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "35:352--35:363",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1393",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1393",
abstract = "In this work, we approximate a diffusion process by
its Euler scheme and we study the convergence of the
density of the marginal laws. We improve previous
estimates especially for small time.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Euler scheme; Malliavin calculus; rate of convergence;
stochastic differential equation",
}
@Article{Marcus:2008:IDG,
author = "Michael Marcus and Jay Rosen",
title = "Infinite Divisibility of {Gaussian} Squares with
Non-zero Means",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "36:364--36:376",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1389",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1389",
abstract = "We give necessary and sufficient conditions for a
Gaussian vector with non-zero mean, to have infinitely
divisible squares for all scalar multiples of the mean,
and show how the this vector is related to the local
times of a Markov chain determined by the covariance
matrix of the Gaussian vector. Our results add to
results of Griffiths, Bapat, Eisenbaum and Kaspi.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Gaussian vectors, infinite divisibility, Markov
chains",
}
@Article{Pete:2008:NPI,
author = "Gabor Pete",
title = "A note on percolation on {$ Z^d $}: isoperimetric
profile via exponential cluster repulsion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "37:377--37:392",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1390",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1390",
abstract = "We show that for all $ p > p_c(\mathbb {Z}^d) $
percolation parameters, the probability that the
cluster of the origin is finite but has at least $t$
vertices at distance one from the infinite cluster is
exponentially small in $t$. We use this to give a short
proof of the strongest version of the important fact
that the isoperimetric profile of the infinite cluster
basically coincides with the profile of the original
lattice. This implies, e.g., that simple random walk on
the largest cluster of a finite box $ [ - n, n]^d$ with
high probability has $ L^\infty $-mixing time $ \Theta
(n^2)$, and that the heat kernel (return probability)
on the infinite cluster a.s. decays like $ p_n(o, o) =
O(n^{-d / 2})$. Versions of these results have been
proven by Benjamini and Mossel (2003), Mathieu and Remy
(2004), Barlow (2004) and Rau (2006). For general
infinite graphs, we prove that anchored isoperimetric
properties survive supercritical percolation, provided
that the probability of the cluster of the origin being
finite with large boundary decays rapidly; this is the
case for a large class of graphs when $p$ is close to
1. As an application (with the help of some entropy
inequalities), we give a short conceptual proof of a
theorem of Angel, Benjamini, Berger and Peres (2006):
the infinite percolation cluster of a wedge in $
\mathbb {Z}^3$ is a.s. transient whenever the wedge
itself is transient.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Flury:2008:NBL,
author = "Markus Flury",
title = "A note on the ballistic limit of random motion in a
random potential",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "38:393--38:400",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1394",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1394",
abstract = "It has been shown that certain types of random walks
in random potentials and Brownian motion in Poissonian
potentials undergo a phase transition from
sub-ballistic to ballistic behavior when the strength
of the underlying drift is increased. The ballistic
behavior has been manifested by indicating a limiting
area for the normalized motion. In the present article,
we provide a refined description of this limiting area
with a further development for the case of rotation
invariant Poissonian potentials.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "RWRP, random walk, random potential, Brownian motion,
Poissonian potential, ballistic phase, ballistic
limit",
}
@Article{Hofmann-Credner:2008:WTR,
author = "Katrin Hofmann-Credner and Michael Stolz",
title = "{Wigner} theorems for random matrices with dependent
entries: Ensembles associated to symmetric spaces and
sample covariance matrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "39:401--39:414",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1395",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1395",
abstract = "It is a classical result of Wigner that for an
Hermitian matrix with independent entries on and above
the diagonal, the mean empirical eigenvalue
distribution converges weakly to the semicircle law as
matrix size tends to infinity. In this paper, we prove
analogs of Wigner's theorem for random matrices taken
from all infinitesimal versions of classical symmetric
spaces. This is a class of models which contains those
studied by Wigner and Dyson, along with seven others
arising in condensed matter physics. Like Wigner's, our
results are universal in that they only depend on
certain assumptions about the moments of the matrix
entries, but not on the specifics of their
distributions. What is more, we allow for a certain
amount of dependence among the matrix entries, in the
spirit of a recent generalization of Wigner's theorem,
due to Schenker and Schulz-Baldes. As a byproduct, we
obtain a universality result for sample covariance
matrices with dependent entries.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "random matrices, symmetric spaces, semicircle law,
Wigner, Marcenko-Pastur, Wishart, sample covariance
matrices, dependent random variables, density of
states, universality",
}
@Article{Kargin:2008:AGS,
author = "Vladislav Kargin",
title = "On Asymptotic Growth of the Support of Free
Multiplicative Convolutions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "40:415--40:421",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1396",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1396",
abstract = "Let $ \mu $ be a compactly supported probability
measure on $ \mathbb {R}^+ $ with expectation $1$ and
variance $ V.$ Let $ \mu_n$ denote the $n$-time free
multiplicative convolution of measure $ \mu $ with
itself. Then, for large $n$ the length of the support
of $ \mu_n$ is asymptotically equivalent to $ e V n$,
where $e$ is the base of natural logarithms, $ e = 2.71
\ldots $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Free probability, free multiplicative convolution",
}
@Article{Luschgy:2008:MEL,
author = "Harald Luschgy and Gilles Pag{\`e}s",
title = "Moment estimates for {L{\'e}vy} Processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "41:422--41:434",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1397",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1397",
abstract = "For real L{\'e}vy processes $ (X_t)_{t \geq 0} $
having no Brownian component with Blumenthal-Getoor
index $ \beta $, the estimate $ E \sup_{s \leq t} |X_s
- a_p s|^p \leq C_p t $ for every $ t \in [0, 1] $ and
suitable $ a_p \in R $ has been established by Millar
for $ \beta < p \leq 2 $ provided $ X_1 \in L^p $. We
derive extensions of these estimates to the cases $ p >
2 $ and $ p \leq \beta $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "alpha-stable process; L{\'e}vy measure; L{\'e}vy
process increment; Meixner process.; Normal Inverse
Gaussian process; tempered stable process",
}
@Article{Kosters:2008:SOC,
author = "Holger K{\"o}sters",
title = "On the Second-Order Correlation Function of the
Characteristic Polynomial of a Real Symmetric {Wigner}
Matrix",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "42:435--42:447",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1400",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1400",
abstract = "We consider the asymptotic behaviour of the
second-order correlation function of the characteristic
polynomial of a real symmetric random matrix. Our main
result is that the existing result for a random matrix
from the Gaussian Orthogonal Ensemble, obtained by
Br{\'e}zin and Hikami (2001), essentially continues to
hold for a general real symmetric Wigner matrix. To
obtain this result, we adapt the approach by G{\"o}tze
and K{\"o}sters (2008), who proved the analogous result
for the Hermitian case.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Alberts:2008:IPC,
author = "Tom Alberts and Michael Kozdron",
title = "Intersection probabilities for a chordal {SLE} path
and a semicircle",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "43:448--43:460",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1399",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1399",
abstract = "We derive a number of estimates for the probability
that a chordal SLE$_\kappa $ path in the upper half
plane $ \mathbb {H}$ intersects a semicircle centred on
the real line. We prove that if $ 0 < \kappa < 8$ and $
\gamma : [0, \infty) \to \overline {\mathbb {H}}$ is a
chordal SLE$_\kappa $ in $ \mathbb {H}$ from $0$ to $
\infty $, then $ P \{ \gamma [0, \infty) \cap \mathcal
{C}(x; r x) \neq \emptyset \} \asymp r^{4a - 1}$ where
$ a = 2 / \kappa $ and $ \mathcal {C}(x; r x)$ denotes
the semicircle centred at $ x > 0$ of radius $ r x$, $
00$. For $ 4 < \kappa < 8$, we also estimate the
probability that an entire semicircle on the real line
is swallowed at once by a chordal SLE$_\kappa $ path in
$ \mathbb {H}$ from $0$ to $ \infty $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Hausdorff dimension; intersection probability;
restriction property; Schramm-Loewner evolution;
Schwarz-Christoffel transformation; swallowing time",
}
@Article{Goldschmidt:2008:FRP,
author = "Christina Goldschmidt and James Martin and Dario
Spano",
title = "Fragmenting random permutations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "44:461--44:474",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1402",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1402",
abstract = "{\bf Problem 1.5.7 from Pitman's Saint-Flour lecture
notes:} Does there exist for each $n$ a fragmentation
process $ (\Pi_{n, k}, 1 \leq k \leq n)$ such that $
\Pi_{n, k}$ is distributed like the partition generated
by cycles of a uniform random permutation of $ \{ 1, 2,
\ldots, n \} $ conditioned to have $k$ cycles? We show
that the answer is yes. We also give a partial
extension to general exchangeable Gibbs partitions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Fragmentation process, random permutation, Gibbs
partition, Chinese restaurant process",
}
@Article{Stenflo:2008:PSL,
author = "{\"O}rjan Stenflo",
title = "Perfect sampling from the limit of deterministic
products of stochastic matrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "45:474--45:481",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1409",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1409",
abstract = "We illustrate how a technique from the theory of
random iterations of functions can be used within the
theory of products of matrices. Using this technique we
give a simple proof of a basic theorem about the
asymptotic behavior of (deterministic) ``backwards
products'' of row-stochastic matrices and present an
algorithm for perfect sampling from the limiting common
row-vector (interpreted as a
probability-distribution).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Perfect sampling, Stochastic matrices, Markov Chain
Monte Carlo, Iterated Function Systems",
}
@Article{Breton:2008:EBN,
author = "Jean-Christophe Breton and Ivan Nourdin",
title = "Error bounds on the non-normal approximation of
{Hermite} power variations of fractional {Brownian}
motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "46:482--46:493",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1415",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1415",
abstract = "Let $ q \geq 2 $ be a positive integer, $B$ be a
fractional Brownian motion with Hurst index $ H \in (0,
1)$, $Z$ be an Hermite random variable of index $q$,
and $ H_q$ denote the $q$ th Hermite polynomial. For
any $ n \geq 1$, set $ V_n = \sum_{k = 0}^{n - 1}
H_q(B_{k + 1} - B_k)$. The aim of the current paper is
to derive, in the case when the Hurst index verifies $
H > 1 - 1 / (2 q)$, an upper bound for the total
variation distance between the laws $ \mathscr
{L}(Z_n)$ and $ \mathscr {L}(Z)$, where $ Z_n$ stands
for the correct renormalization of $ V_n$ which
converges in distribution towards $Z$. Our results
should be compared with those obtained recently by
Nourdin and Peccati (2007) in the case where $ H < 1 -
1 / (2 q)$, corresponding to the case where one has
normal approximation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Fractional Brownian motion; Hermite power variation;
Hermite random variable; Multiple stochastic integrals;
Non-central limit theorem; Total variation distance",
}
@Article{Millan:2008:RGL,
author = "Juan Carlos Pardo Millan",
title = "On the rate of growth of {L{\'e}vy} processes with no
positive jumps conditioned to stay positive",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "47:494--47:506",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1414",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1414",
abstract = "In this note, we study the asymptotic behaviour of
L{\'e}vy processes with no positive jumps conditioned
to stay positive and some related processes. In
particular, we establish an integral test for the lower
envelope at $0$ and at $ + \infty $ and an analogue of
Khintchin's law of the iterated logarithm at 0 and at $
+ \infty $, for the upper envelope of the reflected
process at its future infimum.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "L{\'e}vy processes conditioned to stay positive,
Future infimum process, First and last passage times,
Occupation times, Rate of growth, Integral tests.",
}
@Article{Yukich:2008:LTM,
author = "Joseph Yukich",
title = "Limit theorems for multi-dimensional random
quantizers",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "48:507--48:517",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1418",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1418",
abstract = "We consider the $r$-th power quantization error
arising in the optimal approximation of a
$d$-dimensional probability measure $P$ by a discrete
measure supported by the realization of $n$ i.i.d.
random variables $ X_1, \ldots {}, X_n$. For all $ d
\geq 1$ and $ r \in (0, \infty)$ we establish mean and
variance asymptotics as well as central limit theorems
for the $r$-th power quantization error. Limiting means
and variances are expressed in terms of the densities
of $P$ and $ X_1$. Similar convergence results hold for
the random point measures arising by placing at each $
X_i, 1 \leq i \leq n, $ a mass equal to the local
distortion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "central limit theorems; laws of large numbers;
Quantization; stabilization",
}
@Article{Jiang:2008:DRF,
author = "Thomas Jiang and Kun-Lin Kuo",
title = "Distribution of a random functional of a
{Ferguson--Dirichlet} process over the unit sphere",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "49:518--49:525",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1416",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1416",
abstract = "Jiang, Dickey, and Kuo [12] gave the multivariate
c-characteristic function and showed that it has
properties similar to those of the multivariate Fourier
transformation. We first give the multivariate
c-characteristic function of a random functional of a
Ferguson--Dirichlet process over the unit sphere. We
then find out its probability density function using
properties of the multivariate c-characteristic
function. This new result would generalize that given
by [11].",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "c-characteristic function; Ferguson--Dirichlet
process",
}
@Article{Abreu:2008:FGG,
author = "Victor Perez Abreu and Noriyoshi Sakuma",
title = "Free Generalized Gamma Convolutions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "50:526--50:539",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1413",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1413",
abstract = "The so-called Bercovici-Pata bijection maps the set of
classical infinitely divisible laws to the set of free
infinitely divisible laws. The purpose of this work is
to study the free infinitely divisible laws
corresponding to the classical Generalized Gamma
Convolutions (GGC). Characterizations of their free
cumulant transforms are derived as well as free
integral representations with respect to the free Gamma
process. A random matrix model for free GGC is built
consisting of matrix random integrals with respect to a
classical matrix Gamma process. Nested subclasses of
free GGC are shown to converge to the free stable class
of distributions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Free probability; generalized gamma convolutions;
infinitely divisible distribution; random matrices",
}
@Article{Jagers:2008:GBP,
author = "Peter Jagers and Andreas Lager{\aa}s",
title = "General branching processes conditioned on extinction
are still branching processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "51:540--51:547",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1419",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1419",
abstract = "It is well known that a simple, supercritical
Bienaym{\'e}-Galton--Watson process turns into a
subcritical such process, if conditioned to die out. We
prove that the corresponding holds true for general,
multi-type branching, where child-bearing may occur at
different ages, life span may depend upon reproduction,
and the whole course of events is thus affected by
conditioning upon extinction.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Crump-Mode-Jagers process; extinction; general
branching process; multi-type branching process;
subcritical; supercritical",
}
@Article{Lalley:2008:OCM,
author = "Steven Lalley and George Kordzakhia",
title = "An oriented competition model on {$ Z_+^2 $}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "52:548--52:561",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1422",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1422",
abstract = "We consider a two-type oriented competition model on
the first quadrant of the two-dimensional integer
lattice. Each vertex of the space may contain only one
particle of either Red type or Blue type. A vertex
flips to the color of a randomly chosen southwest
nearest neighbor at exponential rate 2. At time zero
there is one Red particle located at $ (1, 0) $ and one
Blue particle located at $ (0, 1) $. The main result is
a partial shape theorem: Denote by $ R (t) $ and $ B
(t) $ the red and blue regions at time $t$. Then (i)
eventually the upper half of the unit square contains
no points of $ B (t) / t$, and the lower half no points
of $ R (t) / t$; and (ii) with positive probability
there are angular sectors rooted at $ (1, 1)$ that are
eventually either red or blue. The second result is
contingent on the uniform curvature of the boundary of
the corresponding Richardson shape.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "competition, shape theorem, first passage
percolation",
}
@Article{VanHandel:2008:DTN,
author = "Ramon {Van Handel}",
title = "Discrete time nonlinear filters with informative
observations are stable",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "53:562--53:575",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1423",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1423",
abstract = "The nonlinear filter associated with the discrete time
signal-observation model $ (X_k, Y_k) $ is known to
forget its initial condition as $ k \to \infty $
regardless of the observation structure when the signal
possesses sufficiently strong ergodic properties.
Conversely, it stands to reason that if the
observations are sufficiently informative, then the
nonlinear filter should forget its initial condition
regardless of any properties of the signal. We show
that for observations of additive type $ Y_k = h(X_k) +
\xi_k $ with invertible observation function $h$ (under
mild regularity assumptions on $h$ and on the
distribution of the noise $ \xi_k$), the filter is
indeed stable in a weak sense without any assumptions
at all on the signal process. If the signal satisfies a
uniform continuity assumption, weak stability can be
strengthened to stability in total variation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "asymptotic stability; hidden Markov models; nonlinear
filtering; prediction",
}
@Article{Muller:2008:RBM,
author = "Sebastian M{\"u}ller",
title = "Recurrence for branching {Markov} chains",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "54:576--54:605",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1424",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1424",
abstract = "The question of recurrence and transience of branching
Markov chains is more subtle than for ordinary Markov
chains; they can be classified in transience, weak
recurrence, and strong recurrence. We review criteria
for transience and weak recurrence and give several new
conditions for weak recurrence and strong recurrence.
These conditions make a unified treatment of known and
new examples possible and provide enough information to
distinguish between weak and strong recurrence. This
represents a step towards a general classification of
branching Markov chains. In particular, we show that in
homogeneous cases weak recurrence and strong recurrence
coincide. Furthermore, we discuss the generalization of
positive and null recurrence to branching Markov chains
and show that branching random walks on $Z$ are either
transient or positive recurrent.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "spectral radius, branching Markov chains, recurrence,
transience, strong recurrence, positive recurrence",
}
@Article{Kink:2008:MZS,
author = "Peter Kink",
title = "A martingale on the zero-set of a holomorphic
function",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "55:606--55:613",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1425",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1425",
abstract = "We give a simple probabilistic proof of the classical
fact from complex analysis that the zeros of a
holomorphic function of several variables are never
isolated and that they are not contained in any compact
set. No facts from complex analysis are assumed other
than the Cauchy-Riemann definition. From stochastic
analysis only the Ito formula and the standard
existence theorem for stochastic differential equations
are required.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "complex martingales; stochastic differential
equations",
}
@Article{Burdzy:2008:MPP,
author = "Krzysztof Burdzy and David White",
title = "{Markov} processes with product-form stationary
distribution",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "56:614--56:627",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1428",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1428",
abstract = "We consider a continuous time Markov process $ (X, L)
$, where $X$ jumps between a finite number of states
and $L$ is a piecewise linear process with state space
$ \mathbb {R}^d$. The process $L$ represents an
{"inert} {drift"} or {"reinforcement."} We find
sufficient and necessary conditions for the process $
(X, L)$ to have a stationary distribution of the
product form, such that the marginal distribution of
$L$ is Gaussian. We present a number of conjectures for
processes with a similar structure but with continuous
state spaces.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Markov process, stationary distribution, inert drift",
}
@Article{Bertail:2008:EBM,
author = "Patrice Bertail and Emmanuelle Gautherat and Hugo
Harari-Kermadec",
title = "Exponential bounds for multivariate self-normalized
sums",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "57:628--57:640",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1430",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1430",
abstract = "In a non-parametric framework, we establish some
non-asymptotic bounds for self-normalized sums and
quadratic forms in the multivariate case for symmetric
and general random variables. This bounds are entirely
explicit and essentially depends in the general case on
the kurtosis of the Euclidean norm of the standardized
random variables.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Exponential inequalities; Hoeffding inequality.;
multivariate; Self-normalization",
}
@Article{Chigansky:2008:DBM,
author = "Pavel Chigansky and Fima Klebaner",
title = "Distribution of the {Brownian} motion on its way to
hitting zero",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "58:641--58:648",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1432",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1432",
abstract = "For the one-dimensional Brownian motion $ B = (B_t)_{t
\geq 0} $, started at $ x > 0 $, and the first hitting
time $ \tau = \inf \{ t \geq 0 : B_t = 0 \} $, we find
the probability density of $ B_{u \tau } $ for a $ u
\in (0, 1) $, i.e. of the Brownian motion on its way to
hitting zero.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bessel bridge; Brownian bridge; Brownian motion;
heavy-tailed distribution; hitting time; scaled
Brownian excursion",
}
@Article{Enriquez:2008:RSS,
author = "Nathanael Enriquez and Christophe Sabot and Marc Yor",
title = "Renewal series and square-root boundaries for {Bessel}
processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "59:649--59:652",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1436",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1436",
abstract = "We show how a description of Brownian exponential
functionals as a renewal series gives access to the law
of the hitting time of a square-root boundary by a
Bessel process. This extends classical results by
Breiman and Shepp, concerning Brownian motion, and
recovers by different means, extensions for Bessel
processes, obtained independently by Delong and Yor.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bessel processes, renewal series, exponential
functionals, square-root boundaries",
}
@Article{Peskir:2008:LHT,
author = "Goran Peskir",
title = "The Law of the Hitting Times to Points by a Stable
{L{\'e}vy} Process with No Negative Jumps",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "60:653--60:659",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1431",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1431",
abstract = "Let $ X = (X_t)_{t \ge 0} $ be a stable L{\'e}vy
process of index $ \alpha \in (1, 2) $ with the
L{\'e}vy measure $ \nu (d x) = (c / x^{1 + \alpha })
I_{(0, \infty)}(x) d x $ for $ c > 0 $, let $ x > 0 $
be given and fixed, and let $ \tau_x = \inf \{ t > 0 :
X_t = x \} $ denote the first hitting time of $X$ to
$x$. Then the density function $ f_{\tau_x}$ of $
\tau_x$ admits the following series representation:\par
$$ f_{\tau_x}(t) = \frac {x^{\alpha - 1}}{\pi (\Gamma
(\alpha) t)^{2 - 1 / \alpha }} \sum_{n = 1}^\infty
\bigg [( - 1)^{n - 1} \sin (\pi / \alpha) \frac {\Gamma
(n - 1 / \alpha)}{\Gamma (\alpha n - 1)} \Big (\frac
{x^\alpha }{c \Gamma ( - \alpha)t} \Big)^{n - 1} $$
$$ - \sin \Big (\frac {n \pi }{\alpha } \Big) \frac
{\Gamma (1 + n / \alpha)}{n!} \Big (\frac {x^\alpha }{c
\Gamma ( - \alpha)t} \Big)^{(n + 1) / \alpha - 1}
\bigg] $$
for $ t > 0$. In particular, this yields $ f_{\tau_x}(0
+) = 0$ and\par
$$ f_{\tau_x}(t) \sim \frac {x^{\alpha - 1}}{\Gamma
(\alpha - 1), \Gamma (1 / \alpha)} (c \Gamma ( -
\alpha)t)^{-2 + 1 / \alpha } $$
as $ t \rightarrow \infty $. The method of proof
exploits a simple identity linking the law of $ \tau_x$
to the laws of $ X_t$ and $ \sup_{0 \le s \le t} X_s$
that makes a Laplace inversion amenable. A simpler
series representation for $ f_{\tau_x}$ is also known
to be valid when $ x < 0$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stable L{\'e}vy process with no negative jumps,
spectrally positive, first hitting time to a point,
first passage time over a point, supremum process, a
Chapman-Kolmogorov equation of Volterra type, Laplace
transform, the Wiener-Hopf factorisation.",
}
@Article{Osekowski:2008:SIB,
author = "Adam Osekowski",
title = "Sharp inequality for bounded submartingales and their
differential subordinates",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "61:660--61:675",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1433",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1433",
abstract = "Let $ \alpha $ be a fixed number from the interval $
[0, 1] $. We obtain the sharp probability bounds for
the maximal function of the process which is $ \alpha
$-differentially subordinate to a bounded
submartingale. This generalizes the previous results of
Burkholder and Hammack.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "conditional differential subordination; differential
subordination; distribution function; Martingale;
submartingale; tail inequality",
}
@Article{Dumbgen:2008:EBA,
author = "Lutz D{\"u}mbgen and Christoph Leuenberger",
title = "Explicit Bounds for the Approximation Error in
{Benford}'s Law",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "10:99--10:112",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v13-1358",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
MRclass = "60E15 (60F99)",
MRnumber = "2386066 (2009b:60056)",
MRreviewer = "Pieter C. Allaart",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/ecp.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://arxiv.org/abs/0705.4488;
http://ecp.ejpecp.org/article/view/1358;
http://weber.math.washington.edu/~ejpecp/ECP/index.php",
abstract = "Benford's law states that for many random variables $
X > 0 $ its leading digit $ D = D(X) $ satisfies
approximately the equation $ \mathbb {P}(D = d) =
\log_{10}(1 + 1 / d) $ for $ d = 1, 2, \ldots, 9 $.
This phenomenon follows from another, maybe more
intuitive fact, applied to $ Y := \log_{10}X $: For
many real random variables $Y$, the remainder $ U := Y
- \lfloor Y \rfloor $ is approximately uniformly
distributed on $ [0, 1)$. The present paper provides
new explicit bounds for the latter approximation in
terms of the total variation of the density of $Y$ or
some derivative of it. These bounds are an interesting
and powerful alternative to Fourier methods. As a
by-product we obtain explicit bounds for the
approximation error in Benford's law.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Hermite polynomials, Gumbel distribution, Kuiper
distance, normal distribution, total variation, uniform
distribution, Weibull distribution",
}
@Article{Dieker:2009:RBM,
author = "A. B. Dieker and J. Moriarty",
title = "Reflected {Brownian} motion in a wedge:
sum-of-exponential stationary densities",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "1:1--1:16",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1437",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1437",
abstract = "We give necessary and sufficient conditions for the
stationary density of semimartingale reflected Brownian
motion in a wedge to be written as a finite sum of
terms of exponential product form. Relying on geometric
ideas reminiscent of the reflection principle, we give
an explicit formula for the density in such cases.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Reflected Brownian motion with drift -- stationary
distribution -- reflection principle",
}
@Article{Osekowski:2009:SMI,
author = "Adam Osekowski",
title = "Sharp maximal inequality for martingales and
stochastic integrals",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "2:17--2:30",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1438",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1438",
abstract = "Let $ X = (X_t)_{t \geq 0} $ be a martingale and $ H =
(H_t)_{t \geq 0} $ be a predictable process taking
values in $ [ - 1, 1] $. Let $Y$ denote the stochastic
integral of $H$ with respect to $X$. We show that\par
$$ || \sup_{t \geq 0}Y_t||_1 \leq \beta_0 || \sup_{t
\geq 0}|X_t|||_1, $$
where $ \beta_0 = 2, 0856 \ldots $ is the best
possible. Furthermore, if, in addition, $X$ is
nonnegative, then\par
$$ || \sup_{t \geq 0}Y_t||_1 \leq \beta_0^+ || \sup_{t
\geq 0}X_t||_1, $$
where $ \beta_0^+= \frac {14}{9}$ is the best
possible.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Martingale; maximal function; stochastic integral",
}
@Article{Eckhoff:2009:UMM,
author = "Maren Eckhoff and Silke Rolles",
title = "Uniqueness of the mixing measure for a random walk in
a random environment on the positive integers",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "3:31--3:35",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1441",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1441",
abstract = "Consider a random walk in an irreducible random
environment on the positive integers. We prove that the
annealed law of the random walk determines uniquely the
law of the random environment. An application to
linearly edge-reinforced random walk is given.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "random walk in a random environment, mixing measure",
}
@Article{Bjorner:2009:NRF,
author = "Anders Bjorner",
title = "Note: Random-to-front shuffles on trees",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "4:36--4:41",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1445",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1445",
abstract = "A Markov chain is considered whose states are
orderings of an underlying fixed tree and whose
transitions are local ``random-to-front'' reorderings,
driven by a probability distribution on subsets of the
leaves. The eigenvalues of the transition matrix are
determined using Brown's theory of random walk on
semigroups.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "eigenvalue; Markov chain; random walk;
random-to-front; semigroup; shuffle; tree",
}
@Article{Haggstrom:2009:STD,
author = "Olle H{\"a}ggstr{\"o}m and P{\'e}ter Mester",
title = "Some two-dimensional finite energy percolation
processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "5:42--5:54",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1446",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1446",
abstract = "Some examples of translation invariant site
percolation processes on the $ Z^2 $ lattice are
constructed, the most far-reaching example being one
that satisfies uniform finite energy (meaning that the
probability that a site is open given the status of all
others is bounded away from 0 and 1) and exhibits a.s.
the coexistence of an infinite open cluster and an
infinite closed cluster. Essentially the same example
shows that coexistence is possible between an infinite
open cluster and an infinite closed cluster that are
both robust under i.i.d. thinning.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "percolation, uniform finite energy, coexistence",
}
@Article{Mueller:2009:CBS,
author = "Carl Mueller and Zhixin Wu",
title = "A connection between the stochastic heat equation and
fractional {Brownian} motion, and a simple proof of a
result of {Talagrand}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "6:55--6:65",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1403",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See erratum \cite{Mueller:2012:ECB}.",
URL = "http://ecp.ejpecp.org/article/view/1403",
abstract = "We give a new representation of fractional Brownian
motion with Hurst parameter $ H \leq \frac {1}{2} $
using stochastic partial differential equations. This
representation allows us to use the Markov property and
time reversal, tools which are not usually available
for fractional Brownian motion. We then give simple
proofs that fractional Brownian motion does not hit
points in the critical dimension, and that it does not
have double points in the critical dimension. These
facts were already known, but our proofs are quite
simple and use some ideas of L{\'e}vy. {\bf An Erratum
is available in
\url{https://doi.org/10.1214/ECP.v17-1774} ECP volume
{\bf 17} paper number 8.}",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "heat equation, white noise, stochastic partial
differential equations",
}
@Article{Kendall:2009:BCC,
author = "Wilfrid Kendall",
title = "{Brownian} couplings, convexity, and shy-ness",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "7:66--7:80",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1417",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1417",
abstract = "Benjamini, Burdzy and Chen (2007) introduced the
notion of a {\em shy coupling\/}: a coupling of a
Markov process such that, for suitable starting points,
there is a positive chance of the two component
processes of the coupling staying at least a given
positive distance away from each other for all time.
Among other results, they showed that no shy couplings
could exist for reflected Brownian motions in $ C^2 $
bounded convex planar domains whose boundaries contain
no line segments. Here we use potential-theoretic
methods to extend this Benjamini {\em et al.\/}(2007)
result (a) to all bounded convex domains (whether
planar and smooth or not) whose boundaries contain no
line segments, (b) to all bounded convex planar domains
regardless of further conditions on the boundary.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion, coupling",
}
@Article{Deijfen:2009:SRG,
author = "Maria Deijfen",
title = "Stationary random graphs with prescribed iid degrees
on a spatial {Poisson} process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "8:81--8:89",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1448",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1448",
abstract = "Let $ [\mathcal {P}] $ be the points of a Poisson
process on $ R^d $ and $F$ a probability distribution
with support on the non-negative integers. Models are
formulated for generating translation invariant random
graphs with vertex set $ [\mathcal {P}]$ and iid vertex
degrees with distribution $F$, and the length of the
edges is analyzed. The main result is that finite mean
for the total edge length per vertex is possible if and
only if $F$ has finite moment of order $ (d + 1) /
d$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random graphs, degree distribution, Poisson process,
stable matching, stationary model",
}
@Article{Kovchegov:2009:OPB,
author = "Yevgeniy Kovchegov",
title = "Orthogonality and probability: beyond nearest neighbor
transitions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "9:90--9:103",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1447",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1447",
abstract = "In this article, we will explore why Karlin-McGregor
method of using orthogonal polynomials in the study of
Markov processes was so successful for one dimensional
nearest neighbor processes, but failed beyond nearest
neighbor transitions. We will proceed by suggesting and
testing possible fixtures.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "reversible Markov chains, orthogonal polynomials,
Karlin-McGregor representation",
}
@Article{Holmes:2009:SLS,
author = "Mark Holmes",
title = "The scaling limit of senile reinforced random walk",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "10:104--10:115",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1449",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1449",
abstract = "This paper proves that the scaling limit of
nearest-neighbour senile reinforced random walk is
Brownian Motion when the time T spent on the first edge
has finite mean. We show that under suitable
conditions, when T has heavy tails the scaling limit is
the so-called fractional kinetics process, a random
time-change of Brownian motion. The proof uses the
standard tools of time-change and invariance principles
for additive functionals of Markov chains.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Privault:2009:MIS,
author = "Nicolas Privault",
title = "Moment identities for {Skorohod} integrals on the
{Wiener} space and applications",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "11:116--11:121",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1450",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1450",
abstract = "We prove a moment identity on the Wiener space that
extends the Skorohod isometry to arbitrary powers of
the Skorohod integral on the Wiener space. As simple
consequences of this identity we obtain sufficient
conditions for the Gaussianity of the law of the
Skorohod integral and a recurrence relation for the
moments of second order Wiener integrals. We also
recover and extend the sufficient conditions for the
invariance of the Wiener measure under random rotations
given in A. S. {\"U}st{\"u}nel and M. Zakai {\em Prob.
Th. Rel. Fields\/} {\bf 103} (1995), 409--429.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Malliavin calculus, Skorohod integral, Skorohod
isometry, Wiener measure, random isometries.",
}
@Article{vanderHofstad:2009:LLT,
author = "Remco van der Hofstad and Wouter Kager and Tobias
M{\"u}ller",
title = "A local limit theorem for the critical random graph",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "12:122--12:131",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1451",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1451",
abstract = "We consider the limit distribution of the orders of
the $k$ largest components in the Erdos-R{\'e}nyi
random graph inside the {"critical} {window"} for
arbitrary $k$. We prove a local limit theorem for this
joint distribution and derive an exact expression for
the joint probability density function.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random graphs",
}
@Article{Marchal:2009:STE,
author = "Philippe Marchal",
title = "Small time expansions for transition probabilities of
some {L{\'e}vy} processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "13:132--13:142",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1452",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1452",
abstract = "We show that there exist L{\'e}vy processes $ (X_t, t
\geq 0) $ and reals $ y > 0 $ such that for small $t$,
the probability $ P(X_t > y)$ has an expansion
involving fractional powers or more general functions
of $t$. This constrasts with previous results giving
polynomial expansions under additional assumptions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "L{\'e}vy process, transition probability",
}
@Article{Janssen:2009:ESM,
author = "A. J. E. M. Janssen and J. S. H. {Van Leeuwaarden}",
title = "Equidistant sampling for the maximum of a {Brownian}
motion with drift on a finite horizon",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "14:143--14:150",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1453",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1453",
abstract = "A Brownian motion observed at equidistant sampling
points renders a random walk with normally distributed
increments. For the difference between the expected
maximum of the Brownian motion and its sampled version,
an expansion is derived with coefficients in terms of
the drift, the Riemann zeta function and the normal
distribution function.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "equidistant sampling of Brownian motion;
Euler-Maclaurin summation; finite horizon; Gaussian
random walk; maximum; Riemann zeta function",
}
@Article{Duquesne:2009:EPH,
author = "Thomas Duquesne",
title = "An elementary proof of {Hawkes}'s conjecture on
{Galton--Watson} trees",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "15:151--15:164",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1454",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1454",
abstract = "In 1981, J. Hawkes conjectured the exact form of the
Hausdorff gauge function for the boundary of
supercritical Galton--Watson trees under a certain
assumption on the tail at infinity of the total mass of
the branching measure. Hawkes's conjecture has been
proved by T. Watanabe in 2007 as well as other precise
results on fractal properties of the boundary of
Galton--Watson trees. The goal of this paper is to
provide an elementary proof of Hawkes's conjecture
under a less restrictive assumption than in T.
Watanabe's paper, by use of size-biased Galton--Watson
trees introduced by Lyons, Pemantle and Peres in
1995.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "boundary; branching measure; exact Hausdorff measure;
Galton--Watson tree; size-biased tree",
}
@Article{Sheu:2009:NBM,
author = "Yuan-Chung Sheu and Yu-Ting Chen",
title = "A note on $r$-balayages of matrix-exponential
{L{\'e}vy} processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "16:165--16:175",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1456",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1456",
abstract = "In this note we give semi-explicit solutions for
$r$-balayages of matrix-exponential-L{\'e}vy processes.
To this end, we turn to an identity for the joint
Laplace transform of the first entry time and the
undershoot and a semi-explicit solution of the negative
Wiener-Hopf factor. Our result is closely related to
the works by Mordecki in [11], Asmussen, Avram and
Pistorius in [3], Chen, Lee and Sheu in [7], and many
others",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Meckes:2009:QAG,
author = "Elizabeth Meckes",
title = "Quantitative asymptotics of graphical projection
pursuit",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "17:176--17:185",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1457",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1457",
abstract = "There is a result of Diaconis and Freedman which says
that, in a limiting sense, for large collections of
high-dimensional data most one-dimensional projections
of the data are approximately Gaussian. This paper
gives quantitative versions of that result. For a set
of $n$ deterministic vectors $ \{ x_i \} $ in $ R^d$
with $n$ and $d$ fixed, let $ \theta $ be a random
point of the sphere and let $ \mu_\theta $ denote the
random measure which puts equal mass at the projections
of each of the $ x_i$ onto the direction $ \theta $.
For a fixed bounded Lipschitz test function $f$, an
explicit bound is derived for the probability that the
integrals of $f$ with respect to $ \mu_\theta $ and
with respect to a suitable Gaussian distribution differ
by more than $ \epsilon $. A bound is also given for
the probability that the bounded-Lipschitz distance
between these two measures differs by more than $
\epsilon $, which yields a lower bound on the waiting
time to finding a non-Gaussian projection of the $
x_i$, if directions are tried independently and
uniformly.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Projection pursuit, concentration inequalities,
Stein's method, Lipschitz distance",
}
@Article{Lopez-Garcia:2009:CDL,
author = "Marcos Lopez-Garcia",
title = "Characterization of distributions with the length-bias
scaling property",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "18:186--18:191",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1458",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1458",
abstract = "This paper characterizes the density functions of
absolutely continuous positive random variables with
finite expectation whose respective distribution
functions satisfy the so-called length-bias scaling
property.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Length-bias scaling property, Indeterminate moment
problem, theta function",
}
@Article{Kuhn:2009:NSI,
author = "Christoph K{\"u}hn and Maximilian Stroh",
title = "A note on stochastic integration with respect to
optional semimartingales",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "19:192--19:201",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1465",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1465",
abstract = "In this note we discuss the extension of the
elementary stochastic Ito-integral w.r.t. an optional
semimartingale. The paths of an optional semimartingale
possess limits from the left and from the right, but
may have double jumps. This leads to quite interesting
phenomena in integration theory.\par
We find a mathematically tractable domain of general
integrands. The simple integrands are embedded into
this domain. Then, we characterize the integral as the
unique continuous and linear extension of the
elementary integral and show completeness of the space
of integrals. Thus our integral possesses desirable
properties to model dynamic trading gains in
mathematical finance when security price processes
follow optional semimartingales.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "stochastic integration theory, optional
semimartingales, dynamic portfolio choice",
}
@Article{Eisenbaum:2009:OIF,
author = "Nathalie Eisenbaum and Alexander Walsh",
title = "An optimal {It{\^o}} formula for {L{\'e}vy}
processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "20:202--20:209",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1469",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1469",
abstract = "Several It{\^o} formulas have been already established
for L{\'e}vy processes. We explain according to which
criteria they are not {\em optimal\/} and establish an
extended It{\^o} formula that satisfies that criteria.
The interest, in particular, of this formula is to
obtain the explicit decomposition of $ F(X) $, for $X$
L{\'e}vy process and $F$ deterministic function with
locally bounded first order Radon-Nikodym derivatives,
as the sum of a Dirichlet process and a bounded
variation process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "stochastic calculus, L{\'e}vy process, local time,
It{\^o} formula",
}
@Article{Gao:2009:DIM,
author = "Fuqing Gao and Hui Jiang",
title = "Deviation inequalities and moderate deviations for
estimators of parameters in an {Ornstein--Uhlenbeck}
process with linear drift",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "21:210--21:223",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1466",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1466",
abstract = "Some deviation inequalities and moderate deviation
principles for the maximum likelihood estimators of
parameters in an Ornstein--Uhlenbeck process with
linear drift are established by the logarithmic Sobolev
inequality and the exponential martingale method.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Deviation inequality; logarithmic Sobolev inequality;
moderate deviations; Ornstein--Uhlenbeck process",
}
@Article{Lin:2009:ASL,
author = "Fuming Lin",
title = "An Almost Sure Limit Theorem For the Maxima of
Strongly Dependent {Gaussian} Sequences",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "22:224--22:231",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1461",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1461",
abstract = "In this paper, we prove an almost sure limit theorem
for the maxima of strongly dependent Gaussian sequences
under some mild conditions. The result is an expansion
of the weakly dependent result of E. Csaki and K.
Gonchigdanzan.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Almost sure central limit theorem, Strongly dependent
sequence, Logarithmic average",
}
@Article{Wang:2009:FEO,
author = "Jian Wang",
title = "First Eigenvalue of One-dimensional Diffusion
Processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "23:232--23:244",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1464",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1464",
abstract = "We consider the first Dirichlet eigenvalue of
diffusion operators on the half line. A criterion for
the equivalence of the first Dirichlet eigenvalue with
respect to the maximum domain and that to the minimum
domain is presented. We also describe the relationships
between the first Dirichlet eigenvalue of transient
diffusion operators and the standard Muckenhoupt's
conditions for the dual weighted Hardy inequality.
Pinsky's result [17] and Chen's variational formulas
[8] are reviewed, and both provide the original
motivation for this research.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "First Dirichlet eigenvalue, Hardy inequality,
variational formula, transience, recurrence, diffusion
operators",
}
@Article{Dolgopyat:2009:NPA,
author = "Dmitry Dolgopyat and Carlangelo Liverani",
title = "Non-perturbative approach to random walk in
{Markovian} environment",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "24:245--24:251",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1467",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1467",
abstract = "We prove the CLT for a random walk in a dynamical
environment where the states of the environment at
different sites are independent Markov chains.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Central Limit Theorem; Gibbs measures; random
environment; Random walk",
}
@Article{Balan:2009:NFK,
author = "Raluca Balan",
title = "A Note on a {Feynman--Kac}-Type Formula",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "25:252--25:260",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1468",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1468",
abstract = "In this article, we establish a probabilistic
representation for the second-order moment of the
solution of stochastic heat equation, with
multiplicative noise, which is fractional in time and
colored in space. This representation is similar to the
one given in Dalang, Mueller and Tribe (2008) in the
case of an s.p.d.e. driven by a Gaussian noise, which
is white in time. Unlike the formula of Dalang, Mueller
and Tribe (2008) , which is based on the usual Poisson
process, our representation is based on the planar
Poisson process, due to the fractional component of the
noise.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "fractional Brownian motion, stochastic heat equation,
Feynman--Kac formula, planar Poisson process",
}
@Article{Wastlund:2009:EPL,
author = "Johan W{\"a}stlund",
title = "An easy proof of the $ \zeta (2) $ limit in the random
assignment problem",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "26:261--26:269",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1475",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1475",
abstract = "The edges of the complete bipartite graph $ K_{n, n} $
are given independent exponentially distributed costs.
Let $ C_n $ be the minimum total cost of a perfect
matching. It was conjectured by M. M{\'e}zard and G.
Parisi in 1985, and proved by D. Aldous in 2000, that $
C_n $ converges in probability to $ \pi^2 / 6 $. We
give a short proof of this fact, consisting of a proof
of the exact formula $ 1 + 1 / 4 + 1 / 9 + \dots + 1 /
n^2 $ for the expectation of $ C_n $, and a $ O(1 / n)
$ bound on the variance.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "minimum, matching, graph, exponential",
}
@Article{Hough:2009:TTR,
author = "Robert Hough",
title = "Tesselation of a triangle by repeated barycentric
subdivision",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "27:270--27:277",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1471",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1471",
abstract = "Under iterated barycentric subdivision of a triangle,
most triangles become flat in the sense that the
largest angle tends to $ \pi $. By analyzing a random
walk on $ S L_2 (\mathbb {R}) $ we give asymptotics
with explicit constants for the number of flat
triangles and the degree of flatness at a given stage
of subdivision. In particular, we prove analytical
bounds for the upper Lyapunov constant of the walk.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Barycentric subdivision; random walk on a group",
}
@Article{Tudor:2009:HRS,
author = "Ciprian Tudor",
title = "{Hsu--Robbins} and {Spitzer}'s theorems for the
variations of fractional {Brownian} motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "28:278--28:289",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1481",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1481",
abstract = "Using recent results on the behavior of multiple
Wiener-It{\^o} integrals based on Stein's method, we
prove Hsu-Robbins and Spitzer's theorems for sequences
of correlated random variables related to the
increments of the fractional Brownian motion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "multiple stochastic integrals, selfsimilar processes,
fractional Brownian motion, Hermite processes, limit
theorems, Stein's method.",
}
@Article{Biggins:2009:LDR,
author = "J. D. Biggins and D. B. Penman",
title = "Large deviations in randomly coloured random graphs",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "29:290--29:301",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1478",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1478",
abstract = "Models of random graphs are considered where the
presence or absence of an edge depends on the random
types (colours) of its vertices, so that whether or not
edges are present can be dependent. The principal
objective is to study large deviations in the number of
edges. These graphs provide a natural example with two
different non-degenerate large deviation regimes, one
arising from large deviations in the colourings
followed by typical edge placement and the other from
large deviation in edge placement. A secondary
objective is to illustrate the use of a general result
on large deviations for mixtures.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "large deviations, mixture, rate function, random
graphs",
}
@Article{Bernardin:2009:MNP,
author = "Fr{\'e}d{\'e}ric Bernardin and Mireille Bossy and
Miguel Martinez and Denis Talay",
title = "On mean numbers of passage times in small balls of
discretized {It{\^o}} processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "30:302--30:316",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1479",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1479",
abstract = "The aim of this note is to prove estimates on mean
values of the number of times that It{\^o} processes
observed at discrete times visit small balls in $
\mathbb {R}^d $. Our technique, in the innite horizon
case, is inspired by Krylov's arguments in [2, Chap.2].
In the finite horizon case, motivated by an application
in stochastic numerics, we discount the number of
visits by a locally exploding coefficient, and our
proof involves accurate properties of last passage
times at 0 of one dimensional semimartingales.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Diffusion processes, sojourn times, estimates,
discrete times",
}
@Article{Duquesne:2009:RRI,
author = "Thomas Duquesne and Jean-Fran{\c{c}}ois {Le Gall}",
title = "On the re-rooting invariance property of {L{\'e}vy}
trees",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "31:317--31:326",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1484",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1484",
abstract = "We prove a strong form of the invariance under
re-rooting of the distribution of the continuous random
trees called L{\'e}vy trees. This expends previous
results due to several authors.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "continuous tree; re-rooting, L{\'e}vy process; stable
tree",
}
@Article{Khorunzhiy:2009:UBE,
author = "Oleksiy Khorunzhiy and Jean-Fran{\c{c}}ois Marckert",
title = "Uniform bounds for exponential moment of maximum of a
{Dyck} path",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "32:327--32:333",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1486",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1486",
abstract = "Let us consider the maximum $ M(D) $ of a Dyck path
$D$ chosen uniformly in the set of Dyck paths with $ 2
n$ steps. We prove that the exponential moment of $
M(D)$ normalized by the square root of $n$ is bounded
in the limit of infinite $n$. This uniform bound
justifies an assumption used in literature to prove
certain estimates of high moments of large random
matrices.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bernoulli bridge; Dyck paths; random matrices",
}
@Article{Guntuboyina:2009:CSM,
author = "Adityanand Guntuboyina and Hannes Leeb",
title = "Concentration of the spectral measure of large
{Wishart} matrices with dependent entries",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "33:334--33:342",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1483",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1483",
abstract = "We derive concentration inequalities for the spectral
measure of large random matrices, allowing for certain
forms of dependence. Our main focus is on empirical
covariance (Wishart) matrices, but general symmetric
random matrices are also considered.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Wishart matrices, concentration inequalities, spectral
measure",
}
@Article{Janson:2009:SRM,
author = "Svante Janson",
title = "Standard representation of multivariate functions on a
general probability space",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "34:343--34:346",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1477",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1477",
abstract = "It is well-known that a random variable, i.e. a
function defined on a probability space, with values in
a Borel space, can be represented on the special
probability space consisting of the unit interval with
Lebesgue measure. We show an extension of this to
multivariate functions. This is motivated by some
recent constructions of random graphs.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Borel space; random graphs",
}
@Article{Yadin:2009:REM,
author = "Ariel Yadin",
title = "Rate of Escape of the Mixer Chain",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "35:347--35:357",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1474",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1474",
abstract = "The mixer chain on a graph $G$ is the following Markov
chain. Place tiles on the vertices of $G$, each tile
labeled by its corresponding vertex. A {"mixer"} moves
randomly on the graph, at each step either moving to a
randomly chosen neighbor, or swapping the tile at its
current position with some randomly chosen adjacent
tile. We study the mixer chain on $ \mathbb {Z}$, and
show that at time $t$ the expected distance to the
origin is $ t^{3 / 4}$, up to constants. This is a new
example of a random walk on a group with rate of escape
strictly between $ t^{1 / 2}$ and $t$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Maejima:2009:NNC,
author = "Makoto Maejima and Genta Nakahara",
title = "A note on new classes of infinitely divisible
distributions on $ \mathbb {R}^d $",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "36:358--36:371",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1487",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1487",
abstract = "This paper introduces and studies a family of new
classes of infinitely divisible distributions on $
\mathbb {R}^d $ with two parameters. Depending on
parameters, these classes connect the
Goldie-Steutel-Bondesson class and the class of
generalized type $G$ distributions, connect the Thorin
class and the class $M$, connect the class $M$ and the
class of generalized type $G$ distributions. These
classes are characterized by stochastic integral
representations with respect to L{\'e}vy processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{delaPena:2009:EIS,
author = "Victor de la Pe{\~n}a and Guodong Pang",
title = "Exponential inequalities for self-normalized processes
with applications",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "37:372--37:381",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1490",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1490",
abstract = "We prove the following exponential inequality for a
pair of random variables $ (A, B) $ with $ B > 0 $
satisfying the {\em canonical assumption\/}, $ E[\exp
(\lambda A - \frac {\lambda^2}{2} B^2)] \leq 1 $ for $
\lambda \in R $, \par
$$ P \left (\frac {|A|}{\sqrt { \frac {2q - 1}{q}
\left (B^2 + (E[|A|^p])^{2 / p} \right) }} \geq x
\right) \leq \left (\frac {q}{2q - 1} \right)^{\frac
{q}{2q - 1}} x^{- \frac {q}{2q - 1}} e^{-x^2 / 2} $$
for $ x > 0 $, where $ 1 / p + 1 / q = 1 $ and $ p \geq
1 $. Applying this inequality, we obtain exponential
bounds for the tail probabilities for self-normalized
martingale difference sequences. We propose a method of
hypothesis testing for the $ L^p$-norm $ (p \geq 1)$ of
$A$ (in particular, martingales) and some stopping
times. We apply this inequality to the stochastic TSP
in $ [0, 1]^d$ ($ d \geq 2$), connected to the CLT.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "self-normalization, exponential inequalities,
martingales, hypothesis testing, stochastic Traveling
Salesman Problem",
}
@Article{Goncalves:2009:DFZ,
author = "Patricia Goncalves and Milton Jara",
title = "Density fluctuations for a zero-range process on the
percolation cluster",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "38:382--38:395",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1491",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1491",
abstract = "We prove that the density fluctuations for a
zero-range process evolving on the $d$-dimensional
supercritical percolation cluster, with $ d \geq {3}$,
are given by a generalized Ornstein--Uhlenbeck process
in the space of distributions $ \mathscr {S}'(\mathbb
{R}^d)$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "percolation cluster, zero-range process, density
fluctuations",
}
@Article{Nikeghbali:2009:BFR,
author = "Ashkan Nikeghbali and Marc Yor",
title = "The {Barnes} {$G$} function and its relations with
sums and products of generalized {Gamma} convolution
variables",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "39:396--39:411",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1488",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1488",
abstract = "We give a probabilistic interpretation for the Barnes
$G$-function which appears in random matrix theory and
in analytic number theory in the important moments
conjecture due to Keating-Snaith for the Riemann zeta
function, via the analogy with the characteristic
polynomial of random unitary matrices. We show that the
Mellin transform of the characteristic polynomial of
random unitary matrices and the Barnes $G$-function are
intimately related with products and sums of gamma,
beta and log-gamma variables. In particular, we show
that the law of the modulus of the characteristic
polynomial of random unitary matrices can be expressed
with the help of products of gamma or beta variables.
This leads us to prove some non standard type of limit
theorems for the logarithmic mean of the so called
generalized gamma convolutions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Barnes G-function, beta-gamma algebra, generalized
gamma convolution variables, random matrices,
characteristic polynomials of random unitary matrices",
}
@Article{Kargin:2009:SRT,
author = "Vladislav Kargin",
title = "Spectrum of random {Toeplitz} matrices with band
structure",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "40:412--40:423",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1492",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1492",
abstract = "This paper considers the eigenvalues of symmetric
Toeplitz matrices with independent random entries and
band structure. We assume that the entries of the
matrices have zero mean and a uniformly bounded 4th
moment, and we study the limit of the eigenvalue
distribution when both the size of the matrix and the
width of the band with non-zero entries grow to
infinity. It is shown that if the bandwidth\slash size
ratio converges to zero, then the limit of the
eigenvalue distributions is Gaussian. If the ratio
converges to a positive limit, then the distributions
converge to a non-Gaussian distribution, which depends
only on the limit ratio. A formula for the fourth
moment of this distribution is derived.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "random matrices",
}
@Article{Schlemm:2009:FPP,
author = "Eckhard Schlemm",
title = "First-passage percolation on width-two stretches with
exponential link weights",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "41:424--41:434",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1493",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1493",
abstract = "We consider the first-passage percolation problem on
effectively one-dimensional graphs with vertex set $ \{
1, \dots, n \} \times \{ 0, 1 \} $ and
translation-invariant edge-structure. For three of six
non-trivial cases we obtain exact expressions for the
asymptotic percolation rate $ \chi $ by solving certain
recursive distributional equations and invoking results
from ergodic theory to identify $ \chi $ as the
expected asymptotic one-step growth of the
first-passage time from $ (0, 0) $ to $ (n, 0) $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "First-passage percolation, percolation rate, Markov
chains, ergodicity",
}
@Article{Fukushima:2009:LTQ,
author = "Ryoki Fukushima",
title = "From the {Lifshitz} tail to the quenched survival
asymptotics in the trapping problem",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "42:435--42:446",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1497",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1497",
abstract = "The survival problem for a diffusing particle moving
among random traps is considered. We introduce a simple
argument to derive the quenched asymptotics of the
survival probability from the Lifshitz tail effect for
the associated operator. In particular, the upper bound
is proved in fairly general settings and is shown to be
sharp in the case of the Brownian motion among
Poissonian obstacles. As an application, we derive the
quenched asymptotics for the Brownian motion among
traps distributed according to a random perturbation of
the lattice.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Lifshitz tail; random media; survival probability;
Trapping problem",
}
@Article{Hoepfner:2009:EYW,
author = "Reinhard Hoepfner",
title = "An extension of the {Yamada--Watanabe} condition for
pathwise uniqueness to stochastic differential
equations with jumps",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "43:447--43:456",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1499",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1499",
abstract = "We extend the Yamada--Watanabe condition for pathwise
uniqueness to stochastic differential equations with
jumps, in the special case where small jumps are
summable.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "SDE with jumps, pathwise uniqueness, Yamada--Watanabe
condition",
}
@Article{Otobe:2009:TGD,
author = "Yoshiki Otobe",
title = "A type of {Gauss}' divergence formula on {Wiener}
spaces",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "44:457--44:463",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1498",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1498",
abstract = "We will formulate a type of Gauss' divergence formula
on sets of functions which are greater than a specific
value of which boundaries are not regular. Such formula
was first established by L. Zambotti in 2002 with a
profound study of stochastic processes. In this paper
we will give a much shorter and simpler proof for his
formula in a framework of the Malliavin calculus and
give alternate expressions. Our approach also enables
to show that such formulae hold in other Gaussian
spaces.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "divergence formulae on the Wiener spaces, integration
by parts formulae on the Wiener spaces",
}
@Article{Posfai:2009:EMC,
author = "Anna Posfai",
title = "An extension of {Mineka}'s coupling inequality",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "45:464--45:473",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1501",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1501",
abstract = "In this paper we propose a refinement of Mineka's
coupling inequality that gives a better upper bound for
$ d_{TV} \left ({\cal L} \left (W \right), {\cal L}
\left (W + 1 \right) \right) $, where $W$ is a sum of
$n$ independent integer valued random variables, in the
case when $ \text {Var} W \gg n$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "coupon collecting; Mineka coupling; total variation
distance; translated compound Poisson approximation",
}
@Article{Goldstein:2009:BEB,
author = "Larry Goldstein and Qi-Man Shao",
title = "{Berry--Ess{\'e}en} Bounds for Projections of
Coordinate Symmetric Random Vectors",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "46:474--46:485",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1502",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1502",
abstract = "For a coordinate symmetric random vector $ (Y_1,
\ldots, Y_n) = {\bf Y} \in \mathbb {R}^n $, that is,
one satisfying $ (Y_1, \ldots, Y_n) =_d(e_1 Y_1,
\ldots, e_n Y_n) $ for all $ (e_1, \ldots, e_n) \in \{
- 1, 1 \}^n $, for which $ P(Y_i = 0) = 0 $ for all $ i
= 1, 2, \ldots, n $, the following Berry Ess{\'e}en
bound to the cumulative standard normal $ \Phi $ for
the standardized projection $ W_\theta = Y_\theta /
v_\theta $ of $ {\bf Y} $ holds:\par
$$ \sup_{x \in \mathbb {R}}|P(W_\theta \leq x) - \Phi
(x)| \leq 2 \sum_{i = 1}^n | \theta_i|^3 E| X_i|^3 +
8.4 E(V_\theta^2 - 1)^2, $$
where $ Y_\theta = \theta \cdot {\bf Y} $ is the
projection of $ {\bf Y} $ in direction $ \theta \in
\mathbb {R}^n $ with $ || \theta || = 1 $, $ v_\theta =
\sqrt {\mbox {Var}(Y_\theta)}, X_i = |Y_i| / v_\theta $
and $ V_\theta = \sum_{i = 1}^n \theta_i^2 X_i^2 $. As
such coordinate symmetry arises in the study of
projections of vectors chosen uniformly from the
surface of convex bodies which have symmetries with
respect to the coordinate planes, the main result is
applied to a class of coordinate symmetric vectors
which includes cone measure $ {\cal C}_p^n $ on the $
\ell_p^n $ sphere as a special case, resulting in a
bound of order $ \sum_{i = 1}^n | \theta_i|^3 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Borodin:2009:MDB,
author = "Alexei Borodin and Patrik Ferrari and Michael Prahofer
and Tomohiro Sasamoto and Jon Warren",
title = "Maximum of {Dyson} {Brownian} motion and non-colliding
systems with a boundary",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "47:486--47:494",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1503",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1503",
abstract = "We prove an equality-in-law relating the maximum of
GUE Dyson's Brownian motion and the non-colliding
systems with a wall. This generalizes the well known
relation between the maximum of a Brownian motion and a
reflected Brownian motion",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Dyson Brownian motion, reflected Brownian motion,
non-colliding systems with a wall",
}
@Article{Chatterjee:2009:OAS,
author = "Sourav Chatterjee and Michel Ledoux",
title = "An observation about submatrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "48:495--48:500",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1504",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1504",
abstract = "Let $M$ be an arbitrary Hermitian matrix of order $n$,
and $k$ be a positive integer less than $n$. We show
that if $k$ is large, the distribution of eigenvalues
on the real line is almost the same for almost all
principal submatrices of $M$ of order $k$. The proof
uses results about random walks on symmetric groups and
concentration of measure. In a similar way, we also
show that almost all $ k \times n$ submatrices of $M$
have almost the same distribution of singular values.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random matrix, concentration of measure, empirical
distribution, eigenvalue",
}
@Article{Ruggiero:2009:CRI,
author = "Matteo Ruggiero and Stephen Walker",
title = "Countable representation for infinite dimensional
diffusions derived from the two-parameter
{Poisson--Dirichlet} process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "49:501--49:517",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1508",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1508",
abstract = "This paper provides a countable representation for a
class of infinite-dimensional diffusions which extends
the infinitely-many-neutral-alleles model and is
related to the two-parameter Poisson--Dirichlet
process. By means of Gibbs sampling procedures, we
define a reversible Moran-type population process. The
associated process of ranked relative frequencies of
types is shown to converge in distribution to the
two-parameter family of diffusions, which is stationary
and ergodic with respect to the two-parameter
Poisson--Dirichlet distribution. The construction
provides interpretation for the limiting process in
terms of individual dynamics.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Gibbs sampler; infinite-dimensional diffusion;
population process; stationary distribution;
Two-parameter Poisson--Dirichlet process",
}
@Article{Hu:2009:NDP,
author = "Yueyun Hu and Qi-Man Shao",
title = "A note on directed polymers in {Gaussian}
environments",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "50:518--50:528",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1509",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1509",
abstract = "We study the problem of directed polymers in Gaussian
environments in $ \mathbb {Z}^d $ from the viewpoint of
a Gaussian family indexed by the set of random walk
paths. In the zero-temperature case, we give a
numerical bound on the maximum of the Hamiltonian,
whereas in the finite temperature case, we establish an
equivalence between the {"very} strong {disorder"} and
the growth rate of the entropy associated to the
model",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Directed polymer, Gaussian environment",
}
@Article{Hu:2009:SIR,
author = "Yaozhong Hu and David Nualart",
title = "Stochastic integral representation of the {$ L^2 $}
modulus of {Brownian} local time and a central limit
theorem",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "51:529--51:539",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1511",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1511",
abstract = "The purpose of this note is to prove a central limit
theorem for the $ L^2$-modulus of continuity of the
Brownian local time obtained in [3], using techniques
of stochastic analysis. The main ingredients of the
proof are an asymptotic version of Knight's theorem and
the Clark-Ocone formula for the $ L^2$-modulus of the
Brownian local time",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Malliavin calculus, Clark-Ocone formula, Brownian
local time, Knight theorem, central limit theorem,
Tanaka formula",
}
@Article{Liu:2009:IRF,
author = "Wei Liu and Liming Wu",
title = "Identification of the rate function for large
deviations of an irreducible {Markov} chain",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "52:540--52:551",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1512",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1512",
abstract = "For an irreducible Markov chain $ (X_n)_{n \ge 0} $ we
identify the rate function governing the large
deviation estimation of empirical mean $ \frac {1}{n}
\sum_{k = 0}^{n - 1} f(X_k) $ by means of the
Donsker-Varadhan's entropy. That allows us to obtain
the lower bound of large deviations for the empirical
measure $ \frac {1}{n} \sum_{k = 0}^{n - 1}
\delta_{X_k} $ in full generality",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Large deviations, irreducible Markov processes,
Feynman--Kac semigroups",
}
@Article{Jegaraj:2009:STA,
author = "Terence Jegaraj",
title = "Small time asymptotics of {Ornstein--Uhlenbeck}
densities in {Hilbert} spaces",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "53:552--53:559",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1510",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1510",
abstract = "We show that Varadhan's small time asymptotics for
densities of the solution of a stochastic differential
equation in $ \mathbb {R}^n $ carries over to a Hilbert
space-valued Ornstein--Uhlenbeck process whose
transition semigroup is strongly Feller and symmetric.
In the Hilbert space setting, densities are with
respect to a Gaussian invariant measure.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "small time asymptotics, densities,
Ornstein--Uhlenbeck, Hilbert space",
}
@Article{Es-Sarhir:2009:HIF,
author = "Abdelhadi Es-Sarhir and Max-K. von Renesse and Michael
Scheutzow",
title = "{Harnack} Inequality for Functional {SDEs} with
Bounded Memory",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "54:560--54:565",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1513",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1513",
abstract = "We use a coupling method for functional stochastic
differential equations with bounded memory to establish
an analogue of Wang's dimension-free Harnack inequality
\url{http://www.springerlink.com/content/8wllev0xwbe3kvkc/}.
The strong Feller property for the corresponding
segment process is also obtained.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Harnack Inequality, Coupling, Strong Feller Property",
}
@Article{Lalley:2009:GIH,
author = "Steven Lalley and Gregory Lawler and Hariharan
Narayanan",
title = "Geometric Interpretation of Half-Plane Capacity",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "55:566--55:571",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1517",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1517",
abstract = "Schramm-Loewner Evolution describes the scaling limits
of interfaces in certain statistical mechanical
systems. These interfaces are geometric objects that
are not equipped with a canonical parametrization. The
standard parametrization of SLE is via half-plane
capacity, which is a conformal measure of the size of a
set in the reference upper half-plane. This has useful
harmonic and complex analytic properties and makes SLE
a time-homogeneous Markov process on conformal maps. In
this note, we show that the half-plane capacity of a
hull $A$ is comparable up to multiplicative constants
to more geometric quantities, namely the area of the
union of all balls centered in $A$ tangent to $R$, and
the (Euclidean) area of a $1$-neighborhood of $A$ with
respect to the hyperbolic metric.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion, Schramm-Loewner Evolution",
}
@Article{Eichelsbacher:2009:MDT,
author = "Peter Eichelsbacher and Jens Sommerauer",
title = "Moderate deviations for traces of words in a
mult-matrix model",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "56:572--56:586",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1515",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1515",
abstract = "We prove a moderate deviation principle for traces of
words of weakly interacting random matrices defined by
a multi-matrix model with a potential being a small
perturbation of the GUE. The remarkable strength of
high order expansions of the matrix model recently
found by Guionnet and Maurel-Segala is the key fact
that allows us to develop our result and provides also
an alternative proof for a special case of the central
limit theorem for traces of words, studied in the
article of Guionnet and Maurel-Segala (2006).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random matrices, moderate deviations, map
enumeration",
}
@Article{Kulske:2009:SEB,
author = "Christof K{\"u}lske and Marco Formentin",
title = "A symmetric entropy bound on the non-reconstruction
regime of {Markov} chains on {Galton--Watson} trees",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "14",
pages = "57:587--57:596",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v14-1516",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1516",
abstract = "We give a criterion for the non-reconstructability of
tree-indexed $q$-state Markov chains obtained by
broadcasting a signal from the root with a given
transition matrix $M$. Non-reconstruction holds if $
c(M)$ times the expected number of offspring on the
Galton--Watson tree is smaller than 1. Here $ c(M)$ is
an explicit function, which is convex over the set of
$M$'s with a given invariant distribution, that is
defined in terms of a $ (q - 1)$-dimensional
variational problem over symmetric entropies. This
result is equivalent to proving the extremality of the
free boundary condition Gibbs measure within the
corresponding Gibbs-simplex. Our theorem holds for
possibly non-reversible $M$ and its proof is based on a
general recursion formula for expectations of a
symmetrized relative entropy function, which invites
their use as a Lyapunov function. In the case of the
Potts model, the present theorem reproduces earlier
results of the authors, with a simplified proof, in the
case of the symmetric Ising model (where the argument
becomes similar to the approach of Pemantle and Peres)
the method produces the correct reconstruction
threshold), in the case of the (strongly) asymmetric
Ising model where the Kesten-Stigum bound is known to
be not sharp the method provides improved numerical
bounds.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Broadcasting on trees, Gibbs measures, random tree,
Galton--Watson tree, reconstruction problem, free
boundary condition",
}
@Article{Georgiou:2010:SER,
author = "Nicos Georgiou",
title = "Soft edge results for longest increasing paths on the
planar lattice",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "1:1--1:13",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1519",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1519",
abstract = "For two-dimensional last-passage time models of weakly
increasing paths, interesting scaling limits have been
proved for points close the axis (the hard edge). For
strictly increasing paths of Bernoulli($p$) marked
sites, the relevant boundary is the line $ y = p x$. We
call this the soft edge to contrast it with the hard
edge. We prove laws of large numbers for the maximal
cardinality of a strictly increasing path in the
rectangle $ [p^{-1}n - x n^a] \times [n]$ as the
parameters $a$ and $x$ vary. The results change
qualitatively as $a$ passes through the value $ 1 /
2$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bernoulli matching model; Discrete TASEP; increasing
paths; last passage model; soft edge; weak law of large
numbers",
}
@Article{Dirr:2010:LP,
author = "Nicolas Dirr and Patrick Dondl and Geoffrey Grimmett
and Alexander Holroyd and Michael Scheutzow",
title = "{Lipschitz} percolation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "2:14--2:21",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1521",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1521",
abstract = "We prove the existence of a (random) Lipschitz
function $ F : \mathbb {Z}^{d - 1} \to \mathbb {Z}^+ $
such that, for every $ x \in \mathbb {Z}^{d - 1} $, the
site $ (x, F(x)) $ is open in a site percolation
process on $ \mathbb {Z}^d $. The Lipschitz constant
may be taken to be $1$ when the parameter $p$ of the
percolation model is sufficiently close to $1$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "percolation, Lipschitz embedding, random surface",
}
@Article{Zhou:2010:ASF,
author = "Xiaowen Zhou",
title = "Almost sure finiteness for the total occupation time
of an $ (d, \alpha, \beta)$-superprocess",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "3:22--3:31",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1523",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1523",
abstract = "For $ 0 < \alpha \leq 2 $ and $ 0 < \beta \leq 1 $ let
$X$ be the $ (d, \alpha, \beta)$-superprocess, i.e. the
superprocess with $ \alpha $-stable spatial movement in
$ R^d$ and $ (1 + \beta)$-stable branching. Given that
the initial measure $ X_0$ is Lebesgue on $ R^d$, Iscoe
conjectured in [7] that the total occupational time $
\int_0^\infty X_t(B)d t$ is a.s. finite if and only if
$ d \beta < \alpha $, where $B$ denotes any bounded
Borel set in $ R^d$ with non-empty interior.\par
In this note we give a partial answer to Iscoe's
conjecture by showing that $ \int_0^\infty X_t(B)d t <
\infty $ a.s. if $ 2 d \beta < \alpha $ and, on the
other hand, $ \int_0^\infty X_t(B)d t = \infty $ a.s.
if $ d \beta > \alpha $.\par
For $ 2 d \beta < \alpha $, our result can also imply
the a.s. finiteness of the total occupation time (over
any bounded Borel set) and the a.s. local extinction
for the empirical measure process of the $ (d, \alpha,
\beta)$-branching particle system with Lebesgue initial
intensity measure.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Takeda:2010:FKP,
author = "Masayoshi Takeda",
title = "{Feynman--Kac} Penalisations of Symmetric Stable
Processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "4:32--4:43",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1524",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1524",
abstract = "In K. Yano, Y. Yano and M. Yor (2009), limit theorems
for the one-dimensional symmetric $ \alpha $-stable
process normalized by negative (killing) Feynman--Kac
functionals were studied. We consider the same problem
and extend their results to positive Feynman--Kac
functionals of multi-dimensional symmetric $ \alpha
$-stable processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Feynman--Kac functional; Kato measure; penalisation;
symmetric stable process",
}
@Article{Beffara:2010:SLP,
author = "Vincent Beffara and Sacha Friedli and Yvan Velenik",
title = "Scaling Limit of the Prudent Walk",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "5:44--5:58",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1527",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1527",
abstract = "We describe the scaling limit of the nearest neighbour
prudent walk on $ Z^2 $, which performs steps uniformly
in directions in which it does not see sites already
visited. We show that the scaling limit is given by the
process $ Z_u = \int_0^{3u / 7} (\sigma_1 1_{W(s) \geq
0} \vec {e}_1 + \sigma_2 1_{W(s) \geq 0} \vec {e}_2) d
s $, $ u \in [0, 1] $, where $W$ is the one-dimensional
Brownian motion and $ \sigma_1, \sigma_2$ two random
signs. In particular, the asymptotic speed of the walk
is well-defined in the $ L^1$-norm and equals 3/7.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "prudent self-avoiding walk, brownian motion, scaling
limit, ballistic behaviour, ageing",
}
@Article{Kovchegov:2010:OPM,
author = "Yevgeniy Kovchegov",
title = "Orthogonality and probability: mixing times",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "6:59--6:67",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1525",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1525",
abstract = "We produce the first example of bounding total
variation distance to stationarity and estimating
mixing times via orthogonal polynomials diagonalization
of discrete reversible Markov chains, the
Karlin-McGregor approach.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "orthogonal polynomials, random walks, mixing rates",
}
@Article{Nagahata:2010:NDS,
author = "Yukio Nagahata and Nobuo Yoshida",
title = "A Note on the Diffusive Scaling Limit for a Class of
Linear Systems",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "7:68--7:78",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1530",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1530",
abstract = "We consider a class of continuous-time stochastic
growth models on $d$-dimensional lattice with
non-negative real numbers as possible values per site.
We remark that the diffusive scaling limit proven in
our previous work [NY09a] can be extended to wider
class of models so that it covers the cases of
potlatch/smoothing processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "diffusive scaling limit, linear systems, binary
contact process, potlatch process, smoothing process",
}
@Article{Gnedin:2010:SSM,
author = "Alexander Gnedin",
title = "A Species Sampling Model with Finitely Many Types",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "8:79--8:88",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1532",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1532",
abstract = "A two-parameter family of exchangeable partitions with
a simple updating rule is introduced. The partition is
identified with a randomized version of a standard
symmetric Dirichlet species-sampling model with
finitely many types. A power-like distribution for the
number of types is derived.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "exchangeability, Gibbs partition, succession rule",
}
@Article{Samee:2010:PSF,
author = "Farman Samee",
title = "On the Principle of Smooth Fit for Killed Diffusions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "9:89--9:98",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1531",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1531",
abstract = "We explore the principle of smooth fit in the case of
the discounted optimal stopping problem\par
$$ V(x) = \sup_\tau \, \mathsf {E}_x[e^{- \beta \tau
}G(X_\tau)]. $$
We show that there exists a regular diffusion $X$ and
differentiable gain function $G$ such that the value
function $V$ above fails to satisfy the smooth fit
condition $ V'(b) = G'(b)$ at the optimal stopping
point $b$. However, if the fundamental solutions $ \psi
$ and $ \phi $ of the `killed' generator equation $ L_X
u(x) - \beta u(x) = 0$ are differentiable at $b$ then
the smooth fit condition $ V'(b) = G'(b)$ holds
(whenever $X$ is regular and $G$ is differentiable at
$b$). We give an example showing that this can happen
even when `smooth fit through scale' (in the sense of
the discounted problem) fails.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "concave function; discounted optimal stopping; killed
diffusion process; Optimal stopping; principle of
smooth fit; regular diffusion process; scale function",
}
@Article{Bass:2010:MHT,
author = "Richard Bass",
title = "The measurability of hitting times",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "10:99--10:105",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1535",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See correction \cite{Bass:2011:CMH}.",
URL = "http://ecp.ejpecp.org/article/view/1535",
abstract = "Under very general conditions the hitting time of a
set by a stochastic process is a stopping time. We give
a new simple proof of this fact. The section theorems
for optional and predictable sets are easy corollaries
of the proof.\par
A correction to this paper has been published :
\url{http://www.math.washington.edu/~ejpecp/ECP/viewarticle.php?id=2291&layout=abstract}
Electronic Communications in Probability, Vol. 16
(2011), paper 18.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stopping time, hitting time, progressively measurable,
optional, predictable, debut theorem, section theorem",
}
@Article{Fang:2010:CMD,
author = "Ming Fang and Ofer Zeitouni",
title = "Consistent Minimal Displacement of Branching Random
Walks",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "11:106--11:118",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1533",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1533",
abstract = "Let $ \mathbb {T} $ denote a rooted $b$-ary tree and
let $ \{ S_v \}_{v \in \mathbb {T}}$ denote a branching
random walk indexed by the vertices of the tree, where
the increments are i.i.d. and possess a logarithmic
moment generating function $ \Lambda (\cdot)$. Let $
m_n$ denote the minimum of the variables $ S_v$ over
all vertices at the $n$ th generation, denoted by $
\mathbb {D}_n$. Under mild conditions, $ m_n / n$
converges almost surely to a constant, which for
convenience may be taken to be $0$. With $ \bar S_v =
\max \{ S_w : w$ is on the geodesic connecting the root
to $ v \} $, define $ L_n = \min_{v \in \mathbb {D}_n}
\bar S_v$. We prove that $ L_n / n^{1 / 3}$ converges
almost surely to an explicit constant $ l_0$. This
answers a question of Hu and Shi.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Branching Random Walk; Consistent Minimal
Displacement",
}
@Article{Gurel-Gurevich:2010:FAR,
author = "Ori Gurel-Gurevich and Gideon Amir",
title = "On Fixation of Activated Random Walks",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "12:119--12:123",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1536",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1536",
abstract = "We prove that for the Activated Random Walks model on
transitive unimodular graphs, if there is fixation,
then every particle eventually fixates, almost surely.
We deduce that the critical density is at most 1. Our
methods apply for much more general processes on
unimodular graphs. Roughly put, our result apply
whenever the path of each particle has an automorphism
invariant distribution and is independent of other
particles' paths, and the interaction between particles
is automorphism invariant and local. In particular, we
do not require the particles path distribution to be
Markovian. This allows us to answer a question of Rolla
and Sidoravicius, in a more general setting then had
been previously known (by Shellef).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Activated Random Walks; Interacting Particles System",
}
@Article{Fontbona:2010:MOT,
author = "Joaquin Fontbona and H{\'e}l{\`e}ne Gu{\'e}rin and
Sylvie M{\'e}l{\'e}ard",
title = "Measurability of optimal transportation and strong
coupling of martingale measures",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "13:124--13:133",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1534",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1534",
abstract = "We consider the optimal mass transportation problem in
$ \mathbb {R}^d $ with measurably parameterized
marginals under conditions ensuring the existence of a
unique optimal transport map. We prove a joint
measurability result for this map, with respect to the
space variable and to the parameter. The proof needs to
establish the measurability of some set-valued
mappings, related to the support of the optimal
transference plans, which we use to perform a suitable
discrete approximation procedure. A motivation is the
construction of a strong coupling between orthogonal
martingale measures. By this we mean that, given a
martingale measure, we construct in the same
probability space a second one with a specified
covariance measure process. This is done by pushing
forward the first martingale measure through a
predictable version of the optimal transport map
between the covariance measures. This coupling allows
us to obtain quantitative estimates in terms of the
Wasserstein distance between those covariance
measures.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Measurability of optimal transport. Coupling between
orthogonal martingale measures. Predictable transport
process.",
}
@Article{Basak:2010:BRT,
author = "Aniran Basak and Arup Bose",
title = "Balanced random and {Toeplitz} matrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "14:134--14:148",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1537",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1537",
abstract = "Except for the Toeplitz and Hankel matrices, the
common patterned matrices for which the limiting
spectral distribution (LSD) are known to exist share a
common property --- the number of times each random
variable appears in the matrix is (more or less) the
same across the variables. Thus it seems natural to ask
what happens to the spectrum of the Toeplitz and Hankel
matrices when each entry is scaled by the square root
of the number of times that entry appears in the matrix
instead of the uniform scaling by $ n^{-1 / 2} $. We
show that the LSD of these balanced matrices exist and
derive integral formulae for the moments of the limit
distribution. Curiously, it is not clear if these
moments define a unique distribution",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random matrix, eigenvalues, balanced matrix, moment
method, bounded Lipschitz metric, Carleman condition,
almost sure convergence, convergence in distribution,
uniform integrability.",
}
@Article{Ignatiouk-Robert:2010:MBR,
author = "Irina Ignatiouk-Robert",
title = "{$T$}-{Martin} boundary of reflected random walks on a
half-space",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "15:149--15:161",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1541",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1541",
abstract = "The $t$-Martin boundary of a random walk on a
half-space with reflected boundary conditions is
identified. It is shown in particular that the
$t$-Martin boundary of such a random walk is not stable
in the following sense: for different values of $t$,
the $t$-Martin compactifications are not equivalent.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "t-Martin boundary, Markov chain, stability",
}
@Article{Petrov:2010:RSP,
author = "Leonid Petrov",
title = "Random Strict Partitions and Determinantal Point
Processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "16:162--16:175",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1542",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1542",
abstract = "We present new examples of determinantal point
processes with infinitely many particles. The particles
live on the half-lattice $ \{ 1, 2, \dots \} $ or on
the open half-line $ (0, + \infty) $. The main result
is the computation of the correlation kernels. They
have integrable form and are expressed through the
Euler gamma function (the lattice case) and the
classical Whittaker functions (the continuous case).
Our processes are obtained via a limit transition from
a model of random strict partitions introduced by
Borodin (1997) in connection with the problem of
harmonic analysis for projective characters of the
infinite symmetric group.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "determinantal point process; Macdonald kernel; random
strict partitions",
}
@Article{Raschel:2010:GFM,
author = "Kilian Raschel",
title = "{Green} functions and {Martin} compactification for
killed random walks related to {$ {\rm SU}(3) $}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "17:176--17:190",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1543",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1543",
abstract = "We consider the random walks killed at the boundary of
the quarter plane, with homogeneous non-zero jump
probabilities to the eight nearest neighbors and drift
zero in the interior, and which admit a positive
harmonic polynomial of degree three. For these
processes, we find the asymptotic of the Green
functions along all infinite paths of states, and from
this we deduce that the Martin compactification is the
one-point compactification.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "killed random walks, Green functions, Martin
compactification, uniformization.",
}
@Article{Bojdecki:2010:PSQ,
author = "Tomasz Bojdecki and Luis Gorostiza and Anna
Talarczyk",
title = "Particle systems with quasi-homogeneous initial states
and their occupation time fluctuations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "18:191--18:202",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1547",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1547",
abstract = "We consider particle systems in $R$ with initial
configurations belonging to a class of measures that
obey a quasi-homogeneity property, which includes as
special cases homogeneous Poisson measures and many
deterministic measures (simple example: one atom at
each point of $Z$). The particles move independently
according to an alpha-stable L{\'e}vy process, $ \alpha
> 1$, and we also consider the model where they undergo
critical branching. Occupation time fluctuation limits
of such systems have been studied in the Poisson case.
For the branching system in ``low'' dimension the limit
was characterized by a process called sub-fractional
Brownian motion, and this process was attributed to the
branching because it had appeared only in that case. In
the present more general framework sub-fractional
Brownian motion is more prevalent, namely, it also
appears as a component of the limit for the system
without branching in ``low'' dimension. A new method of
proof, based on the central limit theorem, is used.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "branching; distribution-valued process; limit theorem;
occupation time fluctuation; particle system; stable
process; sub-fractional Brownian motion",
}
@Article{Oliveira:2010:SRH,
author = "Roberto Oliveira",
title = "Sums of random {Hermitian} matrices and an inequality
by {Rudelson}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "19:203--19:212",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1544",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1544",
abstract = "We give a new, elementary proof of a key inequality
used by Rudelson in the derivation of his well-known
bound for random sums of rank-one operators. Our
approach is based on Ahlswede and Winter's technique
for proving operator Chernoff bounds. We also prove a
concentration inequality for sums of random matrices of
rank one with explicit constants.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "concentration inequalities; Khintchine inequalities.;
Random Hermitian matrices",
}
@Article{Attanasio:2010:SFD,
author = "Stefano Attanasio",
title = "Stochastic flows of diffeomorphisms for
one-dimensional {SDE} with discontinuous drift",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "20:213--20:226",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1545",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1545",
abstract = "The existence of a stochastic flow of class $ C^{1,
\alpha } $, for $ \alpha < 1 / 2 $, for a 1-dimensional
SDE will be proved under mild conditions on the
regularity of the drift. The diffusion coefficient is
assumed constant for simplicity, while the drift is an
autonomous BV function with distributional derivative
bounded from above or from below. To reach this result
the continuity of the local time with respect to the
initial datum will also be proved.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stochastic flows, Local time",
}
@Article{Maejima:2010:CMI,
author = "Makoto Maejima and Yohei Ueda",
title = "Compositions of mappings of infinitely divisible
distributions with applications to finding the limits
of some nested subclasses",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "21:227--21:239",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1557",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1557",
abstract = "Let $ \{ X_t^{(\mu)}, t \ge 0 \} $ be a L{\'e}vy
process on $ R^d $ whose distribution at time 1 is $
\mu $, and let $f$ be a nonrandom measurable function
on $ (0, a), 0 < a \leq \infty $. Then we can define a
mapping $ \Phi_f(\mu)$ by the law of $ \int_0^a f(t)d
X_t^{(\mu)}$, from $ \mathfrak D(\Phi_f)$ which is the
totality of $ \mu \in I(R^d)$ such that the stochastic
integral $ \int_0^a f(t)d X_t^{(\mu)}$ is definable,
into a class of infinitely divisible distributions. For
$ m \in N$, let $ \Phi_f^m$ be the $m$ times
composition of $ \Phi_f$ itself. Maejima and Sato
(2009) proved that the limits $ \bigcap_{m = 1}^\infty
\Phi^m_f(\mathfrak D(\Phi^m_f))$ are the same for
several known $f$'s. Maejima and Nakahara (2009)
introduced more general $f$'s. In this paper, the
limits $ \bigcap_{m = 1}^\infty \Phi^m_f(\mathfrak
D(\Phi^m_f))$ for such general $f$'s are investigated
by using the idea of compositions of suitable mappings
of infinitely divisible distributions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "infinitely divisible distribution on $\{\mathbb
R\}^d$, stochastic integral mapping, composition of
mappings, limit of nested subclasses",
}
@Article{Vandenberg-Rodes:2010:LTP,
author = "Alexander Vandenberg-Rodes",
title = "A limit theorem for particle current in the symmetric
exclusion process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "22:240--22:252",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1550",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1550",
abstract = "Using the recently discovered strong negative
dependence properties of the symmetric exclusion
process, we derive general conditions for when the
normalized current of particles between regions
converges to the Gaussian distribution. The main
novelty is that the results do not assume any
translation invariance, and hold for most initial
configurations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "central limit theorem; particle current; stability;
symmetric exclusion process",
}
@Article{Bertoin:2010:TTS,
author = "Jean Bertoin",
title = "A two-time-scale phenomenon in a
fragmentation-coagulation process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "23:253--23:262",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1552",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1552",
abstract = "Consider two urns, $A$ and $B$, where initially $A$
contains a large number $n$ of balls and $B$ is empty.
At each step, with equal probability, either we pick a
ball at random in $A$ and place it in $B$, or
vice-versa (provided of course that $A$, or $B$, is not
empty). The number of balls in $B$ after $n$ steps is
of order $ \sqrt n$, and this number remains
essentially the same after $ \sqrt n$ further steps.
Observe that each ball in the urn $B$ after $n$ steps
has a probability bounded away from $0$ and $1$ to be
placed back in the urn $A$ after $ \sqrt n$ additional
steps. So, even though the number of balls in $B$ does
not evolve significantly between $n$ and $ n + \sqrt
n$, the precise contain of urn $B$ does.\par
This elementary observation is the source of an
interesting two-time-scale phenomenon which we
illustrate using a simple model of
fragmentation-coagulation. Inspired by Pitman's
construction of coalescing random forests, we consider
for every $ n \in \mathbb {N}$ a uniform random tree
with $n$ vertices, and at each step, depending on the
outcome of an independent fair coin tossing, either we
remove one edge chosen uniformly at random amongst the
remaining edges, or we replace one edge chosen
uniformly at random amongst the edges which have been
removed previously. The process that records the sizes
of the tree-components evolves by fragmentation and
coagulation. It exhibits subaging in the sense that
when it is observed after $k$ steps in the regime $ k
\sim t n + s \sqrt n$ with $ t > 0$ fixed, it seems to
reach a statistical equilibrium as $ n \to \infty $;
but different values of $t$ yield distinct
pseudo-stationary distributions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Two-time-scale, fragmentation, coagulation, random
forest, subaging.",
}
@Article{Doring:2010:ART,
author = "Leif D{\"o}ring and Mladen Savov",
title = "An Application of Renewal Theorems to Exponential
Moments of Local Times",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "24:263--24:269",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1558",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1558",
abstract = "In this note we explain two transitions known for
moment generating functions of local times by means of
properties of the renewal measure of a related renewal
equation. The arguments simplify and strengthen results
on the asymptotic behavior in the literature",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Renewal Theorem, Local Times",
}
@Article{Cattiaux:2010:PIC,
author = "Patrick Cattiaux and Arnaud Guillin and Cyril
Roberto",
title = "Poincar{\'e} inequality and the {$ L^p $} convergence
of semi-groups",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "25:270--25:280",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1559",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1559",
abstract = "We prove that for symmetric Markov processes of
diffusion type admitting a ``carr{\'e} du champ'', the
Poincar{\'e} inequality is equivalent to the
exponential convergence of the associated semi-group in
one (resp. all) $ L^p(\mu) $ spaces for $ 1 < p <
\infty $. We also give the optimal rate of convergence.
Part of these results extends to the stationary, not
necessarily symmetric situation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Poincar{\'e} inequality, rate of convergence",
}
@Article{Borovkov:2010:DBM,
author = "Konstantin Borovkov",
title = "On the distribution of the {Brownian} motion process
on its way to hitting zero",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "26:281--26:285",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1555",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1555",
abstract = "We present functional versions of recent results on
the univariate distributions of the process $ V_{x, u}
= x + W_{u \tau (x)}, $ $ 0 \le u \le 1 $, where $
W_\bullet $ is the standard Brownian motion process, $
x > 0 $ and $ \tau (x) = \inf \{ t > 0 : \, W_t = - x
\} $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bessel bridge; Brownian meander; Brownian motion;
hitting time",
}
@Article{Konig:2010:RWC,
author = "Wolfgang K{\"o}nig and Patrick Schmid",
title = "Random walks conditioned to stay in {Weyl} chambers of
type {C} and {D}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "27:286--27:296",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1560",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1560",
abstract = "We construct the conditional versions of a
multidimensional random walk given that it does not
leave the Weyl chambers of type C and of type D,
respectively, in terms of a Doob $h$-transform.
Furthermore, we prove functional limit theorems for the
rescaled random walks. This is an extension of recent
work by Eichelsbacher and Koenig who studied the
analogous conditioning for the Weyl chamber of type A.
Our proof follows recent work by Denisov and Wachtel
who used martingale properties and a strong
approximation of random walks by Brownian motion.
Therefore, we are able to keep minimal moment
assumptions. Finally, we present an alternate function
that is amenable to an $h$-transform in the Weyl
chamber of type C.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Conditional random walks, Doob $h$-transform,
non-colliding probability, harmonic functions,
r{\'e}duite, Weyl chamber",
}
@Article{Sapozhnikov:2010:UBE,
author = "Artem Sapozhnikov",
title = "Upper bound on the expected size of the intrinsic
ball",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "28:297--28:298",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1553",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1553",
abstract = "We give a short proof of Theorem 1.2 (i) from the
paper {"The} Alexander-Orbach conjecture holds in high
{dimensions"} by G. Kozma and A. Nachmias. We show that
the expected size of the intrinsic ball of radius $r$
is at most $ C r$ if the susceptibility exponent is at
most 1. In particular, this result follows if the
so-called triangle condition holds.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "chemical distance; Critical percolation;
high-dimensional percolation; intrinsic ball; triangle
condition",
}
@Article{Bose:2010:SNC,
author = "Arup Bose and Rajat Hazra and Koushik Saha",
title = "Spectral norm of circulant type matrices with heavy
tailed entries",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "29:299--29:313",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1554",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1554",
abstract = "We first study the probabilistic properties of the
spectral norm of scaled eigenvalues of large
dimensional Toeplitz, circulant and symmetric circulant
matrices when the input sequence is independent and
identically distributed with appropriate heavy tails.
When the input sequence is a stationary two sided
moving average process of infinite order, we scale the
eigenvalues by the spectral density at appropriate
ordinates and study the limit for their maximums.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "circulant matrix; eigenvalues; Large dimensional
random matrix; moving average process; power transfer
function; reverse circulant matrix; spectral norm;
symmetric circulant matrix; Toeplitz matrix",
}
@Article{Bardina:2010:WAF,
author = "Xavier Bardina and Carles Rovira and Samy Tindel",
title = "Weak approximation of fractional {SDEs}: the {Donsker}
setting",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "30:314--30:329",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1561",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1561",
abstract = "In this note, we take up the study of weak convergence
for stochastic differential equations driven by a
(Liouville) fractional Brownian motion $B$ with Hurst
parameter $ H \in (1 / 3, 1 / 2)$, initiated in a paper
of Bardina et al. (2010,
\url{http://www.ams.org/mathscinet-getitem?mr=MR2565851}
{\bf MR2565851}). In the current paper, we approximate
the $d$-dimensional fBm by the convolution of a
rescaled random walk with Liouville's kernel. We then
show that the corresponding differential equation
converges in law to a fractional SDE driven by $B$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Weak approximation, Kac-Stroock type approximation,
fractional Brownian motion, rough paths",
}
@Article{Panchenko:2010:DSR,
author = "Dmitry Panchenko",
title = "On the {Dovbysh--Sudakov} representation result",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "31:330--31:338",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1562",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1562",
abstract = "We present a detailed proof of the Dovbysh--Sudakov
representation for symmetric positive definite weakly
exchangeable infinite random arrays, called Gram-de
Finetti matrices, which is based on the representation
result of Aldous and Hoover for arbitrary (not
necessarily positive definite) symmetric weakly
exchangeable arrays.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "exchangeability, spin glasses.",
}
@Article{Albin:2010:NPO,
author = "J. M. P. Albin and Hyemi Choi",
title = "A new proof of an old result by {Pickands}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "32:339--32:345",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1566",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1566",
abstract = "Let $ \{ \xi (t) \}_{t \in [0, h]} $ be a stationary
Gaussian process with covariance function $r$ such that
$ r(t) = 1 - C|t|^{\alpha } + o(|t|^{\alpha })$ as $ t
\to 0$. We give a new and direct proof of a result
originally obtained by Pickands, on the asymptotic
behaviour as $ u \to \infty $ of the probability $ \Pr
\{ \sup_{t \in [0, h]} \xi (t) > u \} $ that the
process $ \xi $ exceeds the level $u$. As a by-product,
we obtain a new expression for Pickands constant $
H_\alpha $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "extremes; Pickands constant; Stationary Gaussian
process",
}
@Article{Chakrabarty:2010:CLT,
author = "Arijit Chakrabarty",
title = "{Central Limit Theorem} for truncated heavy tailed
{Banach} valued random vectors",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "33:346--33:364",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1564",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1564",
abstract = "In this paper the question of the extent to which
truncated heavy tailed random vectors, taking values in
a Banach space, retain the characteristic features of
heavy tailed random vectors, is answered from the point
of view of the central limit theorem.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "heavy tails, truncation, regular variation, central
limit theorem, probability on Banach spaces",
}
@Article{Iksanov:2010:EMF,
author = "Alexander Iksanov and Matthias Meiners",
title = "Exponential Moments of First Passage Times and Related
Quantities for Random Walks",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "34:365--34:375",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1569",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1569",
abstract = "For a zero-delayed random walk on the real line, let $
\tau (x) $, $ N(x) $ and $ \rho (x) $ denote the first
passage time into the interval $ (x, \infty) $, the
number of visits to the interval $ ( - \infty, x] $ and
the last exit time from $ ( - \infty, x] $,
respectively. In the present paper, we provide ultimate
criteria for the finiteness of exponential moments of
these quantities. Moreover, whenever these moments are
finite, we derive their asymptotic behaviour, as $ x
\to \infty $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "first-passage time, last exit time, number of visits,
random walk, renewal theory",
}
@Article{Bianchi:2010:AIS,
author = "Pascal Bianchi and M{\'e}rouane Debbah and Jamal
Najim",
title = "Asymptotic Independence in the Spectrum of the
{Gaussian} Unitary Ensemble",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "35:376--35:395",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1568",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1568",
abstract = "Consider a $ n \times n $ matrix from the Gaussian
Unitary Ensemble (GUE). Given a finite collection of
bounded disjoint real Borel sets $ (\Delta_{i, n}, \ 1
\leq i \leq p) $ with positive distance from one
another, eventually included in any neighbourhood of
the support of Wigner's semi-circle law and properly
rescaled (with respective lengths $ n^{-1} $ in the
bulk and $ n^{-2 / 3} $ around the edges), we prove
that the related counting measures $ {\mathcal
N}_n(\Delta_{i, n}), (1 \leq i \leq p) $, where $
{\mathcal N}_n(\Delta) $ represents the number of
eigenvalues within $ \Delta $, are asymptotically
independent as the size $n$ goes to infinity, $p$ being
fixed. As a consequence, we prove that the largest and
smallest eigenvalues, properly centered and rescaled,
are asymptotically independent; we finally describe the
fluctuations of the ratio of the extreme eigenvalues of
a matrix from the GUE.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "asymptotic independence; eigenvalues; Gaussian unitary
ensemble; Random matrix",
}
@Article{Hu:2010:CLT,
author = "Yaozhong Hu and David Nualart",
title = "Central limit theorem for the third moment in space of
the {Brownian} local time increments",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "36:396--36:410",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1573",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1573",
abstract = "The purpose of this note is to prove a central limit
theorem for the third integrated moment of the Brownian
local time increments using techniques of stochastic
analysis. The main ingredients of the proof are an
asymptotic version of Knight's theorem and the
Clark-Ocone formula for the third integrated moment of
the Brownian local time increments.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion, local time, Clark-Ocone formula",
}
@Article{Unterberger:2010:MES,
author = "Jeremie Unterberger",
title = "Moment estimates for solutions of linear stochastic
differential equations driven by analytic fractional
{Brownian} motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "37:411--37:417",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1574",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1574",
abstract = "As a general rule, differential equations driven by a
multi-dimensional irregular path $ \Gamma $ are solved
by constructing a rough path over $ \Gamma $. The
domain of definition - and also estimates - of the
solutions depend on upper bounds for the rough path;
these general, deterministic estimates are too crude to
apply e.g. to the solutions of stochastic differential
equations with linear coefficients driven by a Gaussian
process with Holder regularity $ \alpha < 1 / 2 $. We
prove here (by showing convergence of Chen's series)
that linear stochastic differential equations driven by
analytic fractional Brownian motion [6, 7] with
arbitrary Hurst index $ \alpha \in (0, 1) $ may be
solved on the closed upper half-plane, and that the
solutions have finite variance.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "H{\"o}lder continuity, Chen series; stochastic
differential equations, fractional Brownian motion,
analytic fractional Brownian motion, rough paths",
}
@Article{Lacoin:2010:MAD,
author = "Hubert Lacoin",
title = "The Martingale approach to disorder irrelevance for
pinning models",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "38:418--38:427",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1572",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1572",
abstract = "This paper presents a very simple and self-contained
proof of disorder irrelevance for inhomogeneous pinning
models with return exponent $ \alpha \in (0, 1 / 2) $.
We also give a new upper bound for the contact fraction
of the disordered model at criticality.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Pinning/Wetting Models, Disordered Models, Harris
Criterion, Relevant Disorder, Renewal Theory",
}
@Article{Balan:2010:ECC,
author = "Raluca Balan and Sana Louhichi",
title = "Explicit Conditions for the Convergence of Point
Processes Associated to Stationary Arrays",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "39:428--39:441",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1563",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1563",
abstract = "In this article, we consider a stationary array of
random variables (which satisfy some asymptotic
independence conditions), and the corresponding
sequence of point processes. Our main result identifies
some explicit conditions for the convergence of the
sequence of point processes in terms of the
probabilistic behavior of the variables in the array.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "infinite divisibility, point process, asymptotic
independence, weak convergence, extremal index",
}
@Article{vandenBerg:2010:ERD,
author = "Jacob van den Berg and Marcelo Hil{\'a}rio and
Alexander Holroyd",
title = "Escape of resources in a distributed clustering
process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "40:442--40:448",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1567",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1567",
abstract = "In a distributed clustering algorithm introduced by
Coffman, Courtois, Gilbert and Piret [1], each vertex
of $ \mathbb {Z}^d $ receives an initial amount of a
resource, and, at each iteration, transfers all of its
resource to the neighboring vertex which currently
holds the maximum amount of resource. In [4] it was
shown that, if the distribution of the initial
quantities of resource is invariant under lattice
translations, then the flow of resource at each vertex
eventually stops almost surely, thus solving a problem
posed in [2]. In this article we prove the existence of
translation-invariant initial distributions for which
resources nevertheless escape to infinity, in the sense
that the final amount of resource at a given vertex is
strictly smaller in expectation than the initial
amount. This answers a question posed in [4].",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Clustering process, random spanning tree",
}
@Article{Markstrom:2010:CPN,
author = "Klas Markstr{\"o}m",
title = "Closure Properties and Negatively Associated Measures
violating the {van den Berg--Kesten} Inequality",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "41:449--41:456",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1575",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1575",
abstract = "We first give an example of a negatively associated
measure which does not satisfy the van den Berg-Kesten
inequality. Next we show that the class of measures
satisfying the van den Berg-Kesten inequality is not
closed under either of conditioning, introduction of
external fields or convex combinations. Finally we show
that this class also includes measure which have rank
sequence which is not logconcave.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Negative correlation, Correlation Inequalities,
Closure properties",
}
@Article{DOvidio:2010:ESF,
author = "Mirko D'Ovidio",
title = "Explicit solutions to fractional differential
equations via generalized gamma convolution",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "42:457--42:474",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1570",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1570",
abstract = "In this paper we deal with Mellin convolution of
generalized Gamma densities which leads to integrals of
modified Bessel functions of the second kind. Such
convolutions allow us to explicitly write the solutions
of the time-fractional diffusion equations involving
the adjoint operators of a square Bessel process and a
Bessel process",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Mellin convolution formula, generalized Gamma r.v.'s,
Stable subordinators, Fox functions, Bessel processes,
Modified Bessel functions",
}
@Article{Best:2010:ASM,
author = "Katharina Best and Peter Pfaffelhuber",
title = "The {Aldous--Shields} model revisited with application
to cellular ageing",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "43:475--43:488",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1581",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1581",
abstract = "In Aldous and Shields (1988) a model for a rooted,
growing random binary tree with edge lengths 1 was
presented. For some $ c > 0 $, an external vertex
splits at rate $ c^{-i} $ (and becomes internal) if its
distance from the root (depth) is $i$. We reanalyse the
tree profile for $ c > 1$, i.e. the numbers of external
vertices in depth $ i = 1, 2, \ldots {}$. Our main
results are concrete formulas for the expectation and
covariance-structure of the profile. In addition, we
present the application of the model to cellular
ageing. Here, we say that nodes in depth $ h + 1$ are
senescent, i.e. do not split. We obtain a limit result
for the proportion of non-senesced vertices for large
$h$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "cellular senescence; Hayflick limit; Random tree;
telomere",
}
@Article{Olivier:2010:DIS,
author = "Wintenberger Olivier",
title = "Deviation inequalities for sums of weakly dependent
time series",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "44:489--44:503",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1577",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1577",
abstract = "In this paper we give new deviation inequalities for
the partial sums of weakly dependent data. The loss
from the independent case is studied carefully. We give
examples of non mixing time series such that dynamical
systems and Bernoulli shifts for whom such deviation
inequality holds. The proofs are based on the blocks
technique and different coupling arguments.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bernoulli shifts; Bernstein's type inequalities;
coupling schemes; expanding maps; Markov chains; weak
dependence",
}
@Article{Freij:2010:POS,
author = "Ragnar Freij and Johan W{\"a}stlund",
title = "Partially ordered secretaries",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "45:504--45:507",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1579",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1579",
abstract = "The elements of a finite nonempty partially ordered
set are exposed at independent uniform times in $ [0,
1] $ to a selector who, at any given time, can see the
structure of the induced partial order on the exposed
elements. The selector's task is to choose online a
maximal element. This generalizes the classical linear
order secretary problem, for which it is known that the
selector can succeed with probability $ 1 / e $ and
that this is best possible. We describe a strategy for
the general problem that achieves success probability
at least $ 1 / e $ for an arbitrary partial order.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "best choice problem; partial order.; secretary
problem",
}
@Article{Osekowski:2010:STI,
author = "Adam Osekowski",
title = "Sharp tail inequalities for nonnegative submartingales
and their strong differential subordinates",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "46:508--46:521",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1582",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1582",
abstract = "Let $ f = (f_n)_{n \geq 0} $ be a nonnegative
submartingale starting from $x$ and let $ g = (g_n)_{n
\geq 0}$ be a sequence starting from $y$ and
satisfying\par
$$ |d g_n| \leq |d f_n|, \quad | \mathbb {E}(d g_n|
\mathcal {F}_{n - 1})| \leq \mathbb {E}(d f_n| \mathcal
{F}_{n - 1}) $$
for $ n \geq 1$. We determine the best universal
constant $ U(x, y)$ such that\par
$$ \mathbb {P}(\sup_n g_n \geq 0) \leq ||f||_1 + U(x,
y). $$
As an application, we deduce a sharp weak type $ (1,
1)$ inequality for the one-sided maximal function of
$g$ and determine, for any $ t \in [0, 1]$ and $ \beta
\in \mathbb {R}$, the number\par
$$ L(x, y, t, \beta) = \inf \{ ||f||_1 : \mathbb
{P}(\sup_n g_n \geq \beta) \geq t \} . $$
The estimates above yield analogous statements for
stochastic integrals in which the integrator is a
nonnegative submartingale. The results extend some
earlier work of Burkholder and Choi in the martingale
setting.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Strong differential subordination; Submartingale;
Weak-type inequality",
}
@Article{Aidekon:2010:TAT,
author = "Elie Aidekon",
title = "Tail asymptotics for the total progeny of the critical
killed branching random walk",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "47:522--47:533",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1583",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1583",
abstract = "We consider a branching random walk on $R$ with a
killing barrier at zero. At criticality, the process
becomes eventually extinct, and the total progeny $Z$
is therefore finite. We show that $ P(Z > n)$ is of
order $ (n \ln^2 (n))^{-1}$, which confirms the
prediction of Addario-Berry and Broutin [1].",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Branching random walk, total progeny.",
}
@Article{Caravenna:2010:LDP,
author = "Francesco Caravenna and Martin Borecki",
title = "Localization for $ (1 + 1)$-dimensional pinning models
with {$ (\nabla + \Delta)$}-interaction",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "48:534--48:548",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1584",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1584",
abstract = "We study the localization/delocalization phase
transition in a class of directed models for a
homogeneous linear chain attracted to a defect line.
The self-interaction of the chain is of mixed gradient
and Laplacian kind, whereas the attraction to the
defect line is of $ \delta $-pinning type, with
strength $ \epsilon \ge 0$. It is known that, when the
self-interaction is purely Laplacian, such models
undergo a {\em non-trivial\/} phase transition: to
localize the chain at the defect line, the reward $
\epsilon $ must be greater than a strictly positive
critical threshold $ \epsilon_c > 0$. On the other
hand, when the self-interaction is purely gradient, it
is known that the transition is {\em trivial\/}: an
arbitrarily small reward $ \epsilon > 0$ is sufficient
to localize the chain at the defect line ($ \epsilon_c
= 0$). In this note we show that in the mixed gradient
and Laplacian case, under minimal assumptions on the
interaction potentials, the transition is always
trivial, that is $ \epsilon_c = 0$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Free Energy; Gradient Interaction; Laplacian
Interaction; Linear Chain Model; Localization
Phenomena; Markov Chain; Phase Transition; Pinning
Model; Polymer Model",
}
@Article{Delyon:2010:CIS,
author = "Bernard Delyon",
title = "Concentration inequalities for the spectral measure of
random matrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "49:549--49:562",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1585",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1585",
abstract = "We give new exponential inequalities for the spectral
measure of random Wishart matrices. These results give
in particular useful bounds when these matrices have
the form $ M = Y Y^T $, in the case where $Y$ is a $ p
\times n$ random matrix with independent enties (weaker
conditions are also proposed), and $p$ and $n$ are
large.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "random matrices; Spectral measure",
}
@Article{Tassy:2010:RIG,
author = "Martin Tassy",
title = "Random interlacements on {Galton--Watson} Trees",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "50:562--50:571",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1586",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1586",
abstract = "We study the critical parameter $ u^* $ of random
interlacements on a Galton--Watson tree conditioned on
the non-extinction event. We show that, for a given law
of a Galton--Watson tree, the value of this parameter
is a.s. constant and non-trivial. We also characterize
this value as the solution of a certain equation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random Interlacement, Galton--Watson tree, critical
behaviour",
}
@Article{Savov:2010:RIL,
author = "Mladen Savov and Matthias Winkel",
title = "Right inverses of {L{\'e}vy} processes: the excursion
measure in the general case",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "15",
pages = "51:572--51:584",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v15-1590",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1590",
abstract = "This article is about right inverses of L{\'e}vy
processes as first introduced by Evans in the symmetric
case and later studied systematically by the present
authors and their co-authors. Here we add to the
existing fluctuation theory an explicit description of
the excursion measure away from the (minimal) right
inverse. This description unifies known formulas in the
case of a positive Gaussian coefficient and in the
bounded variation case. While these known formulas
relate to excursions away from a point starting
negative continuously, and excursions started by a
jump, the present description is in terms of excursions
away from the supremum continued up to a return time.
In the unbounded variation case with zero Gaussian
coefficient previously excluded, excursions start
negative continuously, but the excursion measures away
from the right inverse and away from a point are
mutually singular. We also provide a new construction
and a new formula for the Laplace exponent of the
minimal right inverse.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "L{\'e}vy process, right inverse, subordinator,
fluctuation theory, excursion",
}
@Article{Kuhn:2011:OPN,
author = "Christoph K{\"u}hn and Marc Teusch",
title = "Optional processes with non-exploding realized power
variation along stopping times are l{\`a}gl{\`a}d",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "1:1--1:8",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1591",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1591",
abstract = "We prove that an optional process of non-exploding
realized power variation along stopping times possesses
almost surely l{\`a}gl{\`a}d paths. This result is
useful for the analysis of some imperfect market models
in mathematical finance. In the finance applications
variation naturally appears along stopping times and
not pathwise. On the other hand, if the power variation
were only taken along deterministic points in time, the
assertion would obviously be wrong.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "power variation, path properties, stopping times",
}
@Article{Osekowski:2011:RAD,
author = "Adam Osekowski",
title = "On relaxing the assumption of differential
subordination in some martingale inequalities",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "2:9--2:21",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1593",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1593",
abstract = "Let $X$, $Y$ be continuous-time martingales taking
values in a se\-pa\-rable Hilbert space $ \mathcal
{H}$.\par
(i) Assume that $X$, $Y$ satisfy the condition $ [X,
X]_t \geq [Y, Y]_t$ for all $ t \geq 0$. We prove the
sharp inequalities\par
$$ \sup_t||Y_t||_p \leq (p - 1)^{-1} \sup_t||X_t||_p,
\qquad 1 < p \leq 2, $$
$$ \mathbb {P}(\sup_t|Y_t| \geq 1) \leq \frac
{2}{\Gamma (p + 1)} \sup_t||X_t||_p^p, \qquad 1 \leq p
\leq 2, $$
and for any $ K > 0$ we determine the optimal constant
$ L = L(K)$ depending only on $K$ such that\par
$$ \sup_t ||Y_t||_1 \leq K \sup_t \mathbb {E}|X_t|
\log |X_t| + L(K). $$
(ii) Assume that $X$, $Y$ satisfy the condition $ [X,
X]_\infty - [X, X]_{t-} \geq [Y, Y]_\infty - [Y,
Y]_{t-}$ for all $ t \geq 0$. We establish the sharp
bounds\par
$$ \sup_t||Y_t||_p \leq (p - 1) \sup_t||X_t||_p,
\qquad 2 \leq p < \infty $$
and\par
$$ \mathbb {P}(\sup_t|Y_t| \geq 1) \leq \frac {p^{p -
1}}{2} \sup_t||X_t||_p^p, \qquad 2 \leq p < \infty . $$
\par
This generalizes the previous results of Burkholder,
Suh and the author, who showed the above estimates
under the more restrictive assumption of differential
subordination. The proof is based on Burkholder's
technique and integration method.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "differential subordination; Martingale; moment
inequality; weak-type inequality",
}
@Article{Couronne:2011:CSP,
author = "Olivier Couronn{\'e} and Nathana{\"e}l Enriquez and
Lucas Gerin",
title = "Construction of a short path in high-dimensional first
passage percolation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "3:22--3:28",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1595",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1595",
abstract = "For first passage percolation in $ \mathbb {Z}^d $
with large $d$, we construct a path connecting the
origin to $ \{ x_1 = 1 \} $, whose passage time has
optimal order $ \log d / d$. Besides, an improved lower
bound for the {"diagonal"} speed of the cluster
combined with a result by Dhar (1988) shows that the
limiting shape in FPP with exponential passage times
(and thus that of Eden model) is not the Euclidean ball
in dimension larger than 35.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "first passage percolation; limit shape; time
constant",
}
@Article{Backhausz:2011:LDD,
author = "Agnes Backhausz",
title = "Limit distribution of degrees in random family trees",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "4:29--4:37",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1598",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1598",
abstract = "In a one-parameter model for evolution of random
trees, which also includes the Barabasi-Albert random
tree [1], almost sure behavior and the limiting
distribution of the degree of a vertex in a fixed
position are examined. A functional central limit
theorem is also given. Results about Polya urn models
are applied in the proofs.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "preferential attachment; random trees; urn models",
}
@Article{Tkocz:2011:GMD,
author = "Tomasz Tkocz",
title = "{Gaussian} measures of dilations of convex
rotationally symmetric sets in {$ \mathbb {C}^n $}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "5:38--5:49",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1599",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1599",
abstract = "We consider the complex case of the {\em
S-inequality\/}. It concerns the behaviour of Gaussian
measures of dilations of convex and rotationally
symmetric sets in $ \mathbb {C}^n $. We pose and
discuss a conjecture that among all such sets measures
of cylinders decrease the fastest under dilations. Our
main result in this paper is that this conjecture holds
under the additional assumption that the Gaussian
measure of the sets considered is not greater than some
constant $ c > 0.64 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Gaussian measure, convex bodies, isoperimetric
inequalities",
}
@Article{Defosseux:2011:GLU,
author = "Manon Defosseux",
title = "Generalized {Laguerre} Unitary Ensembles and an
interacting particles model with a wall",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "6:59--6:69",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1602",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1602",
abstract = "We introduce and study a new interacting particles
model with a wall and two kinds of interactions ---
blocking and pushing --- which maintain particles in a
certain order. We show that it involves a random matrix
model.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Gelfand-Tsetlin patterns; interacting particles system
with a wall; interlacing; intertwining; random
matrices",
}
@Article{Ghosh:2011:ASB,
author = "Subhankar Ghosh and Larry Goldstein",
title = "Applications of size biased couplings for
concentration of measures",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "7:70--7:83",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1605",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1605",
abstract = "Let $Y$ be a nonnegative random variable with mean $
\mu $ and finite positive variance $ \sigma^2$, and let
$ Y^s$, defined on the same space as $Y$, have the $Y$
size biased distribution, that is, the distribution
characterized by\par
$$ E[Y f(Y)] = \mu E f(Y^s) \quad \mbox {for all
functions {\em f} for which these expectations exist.}
$$
Under a variety of conditions on the coupling of $Y$
and $ Y^s$, including combinations of boundedness and
monotonicity, concentration of measure inequalities
such as\par
$$ P \left (\frac {Y - \mu }{\sigma } \ge t \right)
\le \exp \left ( - \frac {t^2}{2(A + Bt)} \right) \quad
\mbox {for all $ t \ge 0$ } $$
are shown to hold for some explicit $A$ and $B$ in
\cite{cnm}. Such concentration of measure results are
applied to a number of new examples: the number of
relatively ordered subsequences of a random
permutation, sliding window statistics including the
number of $m$-runs in a sequence of coin tosses, the
number of local maxima of a random function on a
lattice, the number of urns containing exactly one ball
in an urn allocation model, and the volume covered by
the union of $n$ balls placed uniformly over a volume
$n$ subset of $ \mathbb {R}^d$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Hubalek:2011:CSR,
author = "Friedrich Hubalek and Alexey Kuznetsov",
title = "A convergent series representation for the density of
the supremum of a stable process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "8:84--8:95",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1601",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1601",
abstract = "We study the density of the supremum of a strictly
stable L{\'e}vy process. We prove that for almost all
values of the index $ \alpha $ - except for a dense set
of Lebesgue measure zero - the asymptotic series which
were obtained in Kuznetsov (2010) {"On} extrema of
stable {processes"} are in fact absolutely convergent
series representations for the density of the
supremum.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "stable processes, supremum, Mellin transform, double
Gamma function, Liouville numbers, continued
fractions",
}
@Article{Rio:2011:ACM,
author = "Emmanuel Rio",
title = "Asymptotic constants for minimal distance in the
central limit theorem",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "9:96--9:103",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1609",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1609",
abstract = "In this paper, we generalize the asymptotic result of
Ess{\'e}en (1958) concerning the Wasserstein distance
of order one in the mean central limit theorem to the
Wasserstein distances of order $r$ for $ r \in]1,
2]$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Minimal metric, Wasserstein distance, Cornish-Fisher
expansion of first order, Ess{\'e}en's mean central
limit theorem, Global central limit theorem",
}
@Article{Bordenave:2011:SSP,
author = "Charles Bordenave",
title = "On the spectrum of sum and product of non-{Hermitian}
random matrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "10:104--10:113",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1606",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1606",
abstract = "In this note, we revisit the work of T. Tao and V. Vu
on large non-Hermitian random matrices with independent
and identically distributed (i.i.d.) entries with mean
zero and unit variance. We prove under weaker
assumptions that the limit spectral distribution of sum
and product of non-Hermitian random matrices is
universal. As a byproduct, we show that the generalized
eigenvalues distribution of two independent matrices
converges almost surely to the uniform measure on the
Riemann sphere.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "generalized eigenvalues, non-Hermitian random
matrices, spherical law",
}
@Article{Bolthausen:2011:RTM,
author = "Erwin Bolthausen and Jean-Dominique Deuschel and Ofer
Zeitouni",
title = "Recursions and tightness for the maximum of the
discrete, two dimensional {Gaussian} free field",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "11:114--11:119",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1610",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1610",
abstract = "We consider the maximum of the discrete two
dimensional Gaussian free field in a box, and prove the
existence of a (dense) deterministic subsequence along
which the maximum, centered at its mean, is tight. The
method of proof relies on an argument developed by
Dekking and Host for branching random walks with
bounded increments and on comparison results specific
to Gaussian fields.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Gaussian free field. Recursions.",
}
@Article{Chassagneux:2011:NEU,
author = "Jean Fran{\c{c}}ois Chassagneux and Romuald Elie and
Idris Kharroubi",
title = "A note on existence and uniqueness for solutions of
multidimensional reflected {BSDEs}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "12:120--12:128",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1614",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1614",
abstract = "In this note, we provide an innovative and simple
approach for proving the existence of a unique solution
for multidimensional reflected BSDEs associated to
switching problems. Getting rid of a monotonicity
assumption on the driver function, this approach
simplifies and extends the recent results of Hu and
Tang (2008) or Hamadene and Zhang (2010).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "BSDE with oblique reflections; Switching problems",
}
@Article{Miranda:2011:GCL,
author = "Yuri Mejia Miranda and Gordon Slade",
title = "The growth constants of lattice trees and lattice
animals in high dimensions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "13:129--13:136",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1612",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1612",
abstract = "We prove that the growth constants for
nearest-neighbour lattice trees and lattice (bond)
animals on the integer lattice $ \mathbb {Z}^d $ are
asymptotic to $ 2 d e $ as the dimension goes to
infinity, and that their critical one-point functions
converge to $e$. Similar results are obtained in
dimensions $ d > 8$ in the limit of increasingly
spread-out models; in this case the result for the
growth constant is a special case of previous results
of M. Penrose. The proof is elementary, once we apply
previous results of T. Hara and G. Slade obtained using
the lace expansion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "growth constant; lattice animal; lattice tree;
mean-field model",
}
@Article{Demni:2011:KRV,
author = "Nizar Demni",
title = "{Kanter} random variable and positive free stable
distributions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "14:137--14:149",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1608",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1608",
abstract = "According to a representation due to M. Kanter, the
density of some power of a positive stable distribution
is a completely monotone function. In this paper, we
first derive its representative Bernstein measure which
also describes the law of some function of a uniform
random variable, referred to below as the Kanter random
variable. Then, the distribution function of the latter
variable is written down and gives a more explicit
description of the non commutative analogue of positive
stable distributions in the setting of Voiculescu's
free probability theory. Analytic evidences of the
occurrence of the Kanter random variable in both the
classical and the free settings conclude the
exposition.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stable laws, free probability, Fox H-function",
}
@Article{Hahn:2011:TCG,
author = "Marjorie Hahn and Jelena Ryvkina and Kei Kobayashi and
Sabir Umarov",
title = "On time-changed {Gaussian} processes and their
associated {Fokker--Planck--Kolmogorov} equations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "15:150--15:164",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1620",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1620",
abstract = "This paper establishes Fokker--Planck-Kolmogorov type
equations for time-changed Gaussian processes. Examples
include those equations for a time-changed fractional
Brownian motion with time-dependent Hurst parameter and
for a time-changed Ornstein--Uhlenbeck process. The
time-change process considered is the inverse of either
a stable subordinator or a mixture of independent
stable subordinators.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Fokker--Planck equation; fractional Brownian motion;
Gaussian process; inverse subordinator; Kolmogorov
equation; time-change; time-dependent Hurst parameter;
Volterra process",
}
@Article{Jung:2011:IFS,
author = "Paul Jung",
title = "Indicator fractional stable motions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "16:165--16:173",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1611",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1611",
abstract = "Using the framework of random walks in random scenery,
Cohen and Samorodnitsky (2006) introduced a family of
symmetric $ \alpha $-stable motions called local time
fractional stable motions. When $ \alpha = 2$, these
processes are precisely fractional Brownian motions
with $ 1 / 2 < H < 1$. Motivated by random walks in
alternating scenery, we find a complementary family of
symmetric $ \alpha $-stable motions which we call
indicator fractional stable motions. These processes
are complementary to local time fractional stable
motions in that when $ \alpha = 2$, one gets fractional
Brownian motions with $ 0 < H < 1 / 2$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "fractional Brownian motion; local time fractional
stable motion; random reward schema; random walk in
random scenery; self-similar process; stable process",
}
@Article{Depperschmidt:2011:MMM,
author = "Andrej Depperschmidt and Andreas Greven and Peter
Pfaffelhuber",
title = "Marked metric measure spaces",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "17:174--17:188",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1615",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1615",
abstract = "A marked metric measure space (mmm-space) is a triple
$ (X, r, \mu) $, where $ (X, r) $ is a complete and
separable metric space and $ \mu $ is a probability
measure on $ X \times I $ for some Polish space $I$ of
possible marks. We study the space of all (equivalence
classes of) marked metric measure spaces for some fixed
$I$. It arises as a state space in the construction of
Markov processes which take values in random graphs,
e.g. tree-valued dynamics describing randomly evolving
genealogical structures in population models. We derive
here the topological properties of the space of
mmm-spaces needed to study convergence in distribution
of random mmm-spaces. Extending the notion of the
Gromov-weak topology introduced in (Greven,
Pfaffelhuber and Winter, 2009), we define the marked
Gromov-weak topology, which turns the set of mmm-spaces
into a Polish space. We give a characterization of
tightness for families of distributions of random
mmm-spaces and identify a convergence determining
algebra of functions, called polynomials.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Metric measure space, Gromov metric triples, Gromov-
weak topology, Prohorov metric, Population model",
}
@Article{Bass:2011:CMH,
author = "Richard Bass",
title = "Correction to {``The measurability of hitting
times''}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "18:189--18:191",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1627",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See \cite{Bass:2010:MHT}.",
URL = "http://ecp.ejpecp.org/article/view/1627",
abstract = "We correct an error in
\url{http://www.math.washington.edu/~ejpecp/ECP/viewarticle.php?id=2181&layout=abstract}
Electronic Communications in Probability, Vol 15
(2010), paper 10.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stopping time, hitting time, progressively measurable,
optional, predictable, debut theorem, section theorem",
}
@Article{Neunhauserer:2011:FEP,
author = "J{\"o}rg Neunh{\"a}userer",
title = "A family of exceptional parameters for non-uniform
self-similar measures",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "19:192--19:199",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1618",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
URL = "http://ecp.ejpecp.org/article/view/1618",
abstract = "We present plane algebraic curves that have segments
of points for which non uniform self-similar measures
get singular. We calculate appropriate points on the
curves using Mathematica. These points are in the
parameter domain where we generically have absolute
continuity of the measures.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Non-uniform self similar measures, singularity,
algebraic curves",
}
@Article{Graversen:2011:RUC,
author = "Svend-Erik Graversen and Jan Pedersen",
title = "Representations of {Urbanik}'s classes and
multiparameter {Ornstein--Uhlenbeck} processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "20:200--20:212",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1621",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1621",
abstract = "A class of integrals with respect to homogeneous
L{\'e}vy bases on $ \mathbb {R}^k $ is considered. In
the one-dimensional case $ k = 1 $ this class
corresponds to the selfdecomposable distributions.
Necessary and sufficient conditions for existence as
well as some representations of the integrals are
given. Generalizing the one-dimensional case it is
shown that the class of integrals corresponds to
Urbanik's class $ L_{k - 1}(R) $. Finally,
multiparameter Ornstein--Uhlenbeck processes are
defined and studied.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "L{\'e}vy bases; multiparameter Ornstein--Uhlenbeck
processes; stochastic integrals; Urbanik's classes",
}
@Article{Debussche:2011:AFE,
author = "Arnaud Debussche and Michael Hoegele and Peter
Imkeller",
title = "Asymptotic first exit times of the {Chafee--Infante}
equation with small heavy-tailed {L{\'e}vy} noise",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "21:213--21:225",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1622",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1622",
abstract = "This article studies the behavior of stochastic
reaction-diffusion equations driven by additive
regularly varying pure jump L{\'e}vy noise in the limit
of small noise intensity. It is shown that the law of
the suitably renormalized first exit times from the
domain of attraction of a stable state converges to an
exponential law of parameter 1 in a strong sense of
Laplace transforms, including exponential moments. As a
consequence, the expected exit times increase
polynomially in the inverse intensity, in contrast to
Gaussian perturbations, where this growth is known to
be of exponential rate.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "first exit times; regularly varying L{\'e}vy process;
small noise asymptotics; stochastic reaction diffusion
equation with heavy-tailed L{\'e}vy noise",
}
@Article{Ben-Ari:2011:SSM,
author = "Iddo Ben-Ari and Anastasios Matzavinos and Alexander
Roitershtein",
title = "On a species survival model",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "22:226--22:233",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1625",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1625",
abstract = "In this paper we provide some sharp asymptotic results
for a stochastic model of species survival recently
proposed by Guiol, Machado, and Schinazi.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bak-Sneppen model; birth and death process; central
limit theorem; evolution; law of iterated logarithm;
population genetics",
}
@Article{Menozzi:2011:PTM,
author = "Stephane Menozzi",
title = "Parametrix techniques and martingale problems for some
degenerate {Kolmogorov} equations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "23:234--23:250",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1619",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1619",
abstract = "We prove the uniqueness of the martingale problem
associated to some degenerate operators. The key point
is to exploit the strong parallel between the new
technique introduced by Bass and Perkins [BP09] to
prove uniqueness of the martingale problem in the
framework of non- degenerate elliptic operators and the
Mc Kean and Singer [MS67] parametrix approach to the
density expansion that has previously been extended to
the degenerate setting that we consider (see Delarue
and Menozzi [DM10]).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Parametrix techniques, Martingale problem,
hypoelliptic equations",
}
@Article{Peres:2011:RTE,
author = "Yuval Peres and Sebastien Roch",
title = "Reconstruction on Trees: Exponential Moment Bounds for
Linear Estimators",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "24:251--24:261",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1630",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1630",
abstract = "Consider a Markov chain $ (\xi_v)_{v \in V} \in [k]^V
$ on the infinite $b$-ary tree $ T = (V, E)$ with
irreducible edge transition matrix $M$, where $ b \geq
2$, $ k \geq 2$ and $ [k] = \{ 1, \ldots, k \} $. We
denote by $ L_n$ the level-$n$ vertices of $T$. Assume
$M$ has a real second-largest (in absolute value)
eigenvalue $ \lambda $ with corresponding real
eigenvector $ \nu \neq 0$. Letting $ \sigma_v =
\nu_{\xi_v}$, we consider the following root-state
estimator, which was introduced by Mossel and Peres
(2003) in the context of the ``recontruction problem''
on trees: \begin{equation*} S_n = (b\lambda)^{-n}
\sum_{x\in L_n} \sigma_x. \end{equation*} As noted by
Mossel and Peres, when $ b \lambda^2 > 1$ (the
so-called Kesten-Stigum reconstruction phase) the
quantity $ S_n$ has uniformly bounded variance. Here,
we give bounds on the moment-generating functions of $
S_n$ and $ S_n^2$ when $ b \lambda^2 > 1$. Our results
have implications for the inference of evolutionary
trees.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Markov chains on trees, reconstruction problem,
Kesten-Stigum bound, phylogenetic reconstruction",
}
@Article{Tropp:2011:FIM,
author = "Joel Tropp",
title = "{Freedman}'s inequality for matrix martingales",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "25:262--25:270",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1624",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1624",
abstract = "Freedman's inequality is a martingale counterpart to
Bernstein's inequality. This result shows that the
large-deviation behavior of a martingale is controlled
by the predictable quadratic variation and a uniform
upper bound for the martingale difference sequence.
Oliveira has recently established a natural extension
of Freedman's inequality that provides tail bounds for
the maximum singular value of a matrix-valued
martingale. This note describes a different proof of
the matrix Freedman inequality that depends on a deep
theorem of Lieb from matrix analysis. This argument
delivers sharp constants in the matrix Freedman
inequality, and it also yields tail bounds for other
types of matrix martingales. The new techniques are
adapted from recent work by the present author.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Discrete-time martingale, large deviation, probability
inequality, random matrix",
}
@Article{Blath:2011:SEC,
author = "Jochen Blath and Noemi Kurt",
title = "Survival and extinction of caring double-branching
annihilating random walk",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "26:271--26:282",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1631",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1631",
abstract = "Branching annihilating random walk (BARW) is a generic
term for a class of interacting particle systems on $
\mathbb {Z}^d $ in which, as time evolves, particles
execute random walks, produce offspring (on
neighbouring sites) and (instantaneously) disappear
when they meet other particles. Much of the interest in
such models stems from the fact that they typically
lack a monotonicity property called {\em
attractiveness\/}, which in general makes them
exceptionally hard to analyse and in particular highly
sensitive in their qualitative long-time behaviour to
even slight alterations of the branching and
annihilation mechanisms. In this short note, we
introduce so-called {\em caring\/} double-branching
annihilating random walk (cDBARW) on $ \mathbb {Z} $,
and investigate its long-time behaviour. It turns out
that it either allows survival with positive
probability if the branching rate is greater than $ 1 /
2 $, or a.s. extinction if the branching rate is
smaller than $ 1 / 3 $ and (additionally) branchings
are only admitted for particles which have at least one
neighbouring particle (so-called 'cooperative
branching'). Further, we show a.s. extinction for all
branching rates for a variant of this model, where
branching is only allowed if offspring can be placed at
odd distance between each other. It is the latter
(extinction-type) results which seem remarkable, since
they appear to hint at a general extinction result for
a non-trivial parameter range in the so-called
'parity-preserving universality class', suggesting the
existence of a 'true' phase transition. The rigorous
proof of such a non-trivial phase transition remains a
particularly challenging open problem.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Branching Annihilating Random Walk, extinction,
survival, interface duality, swapping voter model",
}
@Article{Junglen:2011:QBA,
author = "Stefan Junglen",
title = "Quantization Balls and Asymptotics of Quantization
Radii for Probability Distributions with Radial
Exponential Tails",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "27:283--27:295",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1629",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1629",
abstract = "In this paper, we provide the sharp asymptotics for
the {\em quantization radius (maximal radius)\/} for a
sequence of {\em optimal quantizers\/} for random
variables $X$ in $ (\mathbb {R}^d, \| \, \cdot \, \|)$
with radial exponential tails. This result sharpens and
generalizes the results developed for the quantization
radius in [4] for $ d > 1$, where the weak asymptotics
is established for similar distributions in the
Euclidean case. Furthermore, we introduce {\em
quantization balls\/}, which provide a more general way
to describe the asymptotic geometric structure of
optimal codebooks, and extend the terminology of the
quantization radius.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Aurzada:2011:MRT,
author = "Frank Aurzada and Hanna D{\"o}ring and Marcel Ortgiese
and Michael Scheutzow",
title = "Moments of recurrence times for {Markov} chains",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "28:296--28:303",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1632",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1632",
abstract = "We consider moments of the return times (or first
hitting times) in an irreducible discrete time discrete
space Markov chain. It is classical that the finiteness
of the first moment of a return time of one state
implies the finiteness of the first moment of the first
return time of any other state. We extend this
statement to moments with respect to a function $f$,
where $f$ satisfies a certain, best possible condition.
This generalizes results of K. L. Chung (1954) who
considered the functions $ f(n) = n^p$ and wondered
``[\ldots{}] what property of the power $ n^p$ lies
behind this theorem [\ldots{}]'' (see Chung (1967), p.
70). We exhibit that exactly the functions that do not
increase exponentially - neither globally nor locally -
fulfill the above statement.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Discrete time Markov chain, recurrence time,
generalized moment",
}
@Article{Barbu:2011:RTP,
author = "Viorel Barbu and Giuseppe {Da Prato} and Luciano
Tubaro",
title = "A Reflection Type Problem for the Stochastic {$2$-D}
{Navier--Stokes} Equations with Periodic Conditions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "29:304--29:313",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1633",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1633",
abstract = "We prove the existence of a solution for the
Kolmogorov equation associated with a reflection
problem for {$2$-D} stochastic Navier--Stokes equations
with periodic spatial conditions and the corresponding
stream flow in a closed ball of a Sobolev space of the
torus $ T^2 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "{$2$-D} stochastic Navier--Stokes equations, Gibbs
measures, Kolmogorov operator",
}
@Article{Dallaporta:2011:NCL,
author = "Sandrine Dallaporta and Van Vu",
title = "A note on the {Central Limit Theorem} for the
Eigenvalue Counting Function of {Wigner} Matrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "30:214--30:322",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1634",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1634",
abstract = "The purpose of this note is to establish a Central
Limit Theorem for the number of eigenvalues of a Wigner
matrix in an interval. The proof relies on the correct
asymptotics of the variance of the eigenvalue counting
function of GUE matrices due to Gustavsson, and its
extension to large families of Wigner matrices by means
of the Tao and Vu Four Moment Theorem and recent
localization results by Erd?s, Yau and Yin.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Central Limit Theorem; eigenvalue counting function;
Four Moment Theorem; localization; random matrices",
}
@Article{Heil:2011:RLB,
author = "Hadrian Heil and Makoto Nakashima",
title = "A Remark on Localization for Branching Random Walks in
Random Environment",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "31:323--31:336",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1603",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1603",
abstract = "We prove a localization-result for branching random
walks in random environment, namely that if the process
does not die out, the most populated site will
infinitely often contain more than a fixed percentage
of the population. This had been proven already before
by Hu and Yoshida, but it is possible to drop their
assumption that particles may not die.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "branching random walk; localization; random
environment",
}
@Article{Fournier:2011:SSH,
author = "Nicolas Fournier and Jacques Printems",
title = "Stability of the stochastic heat equation in {$ L^1
([0, 1]) $}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "32:337--32:352",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1636",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1636",
abstract = "We consider the white-noise driven stochastic heat
equation on $ [0, 1] $ with Lipschitz-continuous drift
and diffusion coefficients. We derive an inequality for
the $ L^1 ([0, 1])$-norm of the difference between two
solutions. Using some martingale arguments, we show
that this inequality provides some estimates which
allow us to study the stability of the solution with
respect the initial condition, the uniqueness of the
possible invariant distribution and the asymptotic
confluence of solutions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Tucci:2011:API,
author = "Gabriel Tucci",
title = "Asymptotic Products of Independent {Gaussian} Random
Matrices with Correlated Entries",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "33:353--33:364",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1635",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1635",
abstract = "In this work we address the problem of determining the
asymptotic spectral measure of the product of
independent, Gaussian random matrices with correlated
entries, as the dimension and the number of
multiplicative terms goes to infinity. More
specifically, let $ \{ X_p(N) \}_{p = 1}^\infty $ be a
sequence of $ N \times N $ independent random matrices
with independent and identically distributed Gaussian
entries of zero mean and variance $ \frac {1}{\sqrt
{N}} $. Let $ \{ \Sigma (N) \}_{N = 1}^\infty $ be a
sequence of $ N \times N $ deterministic and Hermitian
matrices such that the sequence converges in moments to
a compactly supported probability measure $ \sigma $.
Define the random matrix $ Y_p(N) $ as $ Y_p(N) =
X_p(N) \Sigma (N) $. This is a random matrix with
correlated Gaussian entries and covariance matrix $
E(Y_p(N)^*Y_p(N)) = \Sigma (N)^2 $ for every $ p \geq 1
$. The positive definite $ N \times N $ matrix\par
$$ B_n^{1 / (2n)} (N) := \left (Y_1^* (N) Y_2^* (N)
\dots Y_n^*(N) Y_n(N) \dots Y_2 (N) Y_1 (N) \right)^{1
/ (2n)} \to \nu_n $$
converges in distribution to a compactly supported
measure in $ [0, \infty) $ as the dimension of the
matrices $ N \to \infty $. We show that the sequence of
measures $ \nu_n $ converges in distribution to a
compactly supported measure $ \nu_n \to \nu $ as $ n
\to \infty $. The measures $ \nu_n $ and $ \nu $ only
depend on the measure $ \sigma $. Moreover, we deduce
an exact closed-form expression for the measure $ \nu $
as a function of the measure $ \sigma $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Limit Measures; Lyapunov Exponents; MIMO systems;
Random Matrices",
}
@Article{Bourguin:2011:CTG,
author = "Solesne Bourguin and Ciprian Tudor",
title = "Cram{\'e}r theorem for Gamma random variables",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "34:365--34:378",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1639",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1639",
abstract = "In this paper we discuss the following problem: given
a random variable $ Z = X + Y $ with Gamma law such
that $X$ and $Y$ are independent, we want to understand
if then $X$ and $Y$ each follow a Gamma law. This is
related to Cramer's theorem which states that if $X$
and $Y$ are independent then $ Z = X + Y$ follows a
Gaussian law if and only if $X$ and $Y$ follow a
Gaussian law. We prove that Cramer's theorem is true in
the Gamma context for random variables living in a
Wiener chaos of fixed order but the result is not true
in general. We also give an asymptotic variant of our
result.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Cram{\'e}r's theorem, Gamma distribution, multiple
stochastic integrals, limit theorems, Malliavin
calculus",
}
@Article{Rath:2011:TRI,
author = "Balazs Rath and Artem Sapozhnikov",
title = "On the transience of random interlacements",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "35:379--35:391",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1637",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1637",
abstract = "We consider the interlacement Poisson point process on
the space of doubly-infinite $ \mathbb {Z}^d$-valued
trajectories modulo time-shift, tending to infinity at
positive and negative infinite times. The set of
vertices and edges visited by at least one of these
trajectories is the graph induced by the random
interlacements at level $u$ of Sznitman(2010). We prove
that for any $ u > 0$, almost surely, the random
interlacement graph is transient.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "capacity.; intersection of random walks; Random
interlacement; random walk; resistance; transience",
}
@Article{Aurzada:2011:OSE,
author = "Frank Aurzada",
title = "On the one-sided exit problem for fractional
{Brownian} motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "36:392--36:404",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1640",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1640",
abstract = "We consider the one-sided exit problem for fractional
Brownian motion (FBM), which is equivalent to the
question of the distribution of the lower tail of the
maximum of FBM on the unit interval. We improve the
bounds given by Molchan (1999) and shed some light on
the relation to the quantity I studied there.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "First passage time; fractional Brownian motion; lower
tail probability; one-sided barrier problem; one-sided
exit problem; small value probability; survival
exponent",
}
@Article{Bose:2011:HIH,
author = "Arup Bose and Rajat Hazra and Koushik Saha",
title = "Half Independence and half cumulants",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "37:405--37:422",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1651",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1651",
abstract = "The notion of half independence arises in random
matrices and quantum groups. This notion is available
only for elements of a noncommutative probability space
and assumes the existence of all moments. We relate
half independence to a certain class of partitions and
use it to define an appropriate cumulant generating
function and a transform which is closely related to
the characteristic function. This leads to a definition
of half independent convolution of arbitrary
probability measures which is compatible with the
distribution of the sum of half independent elements of
a noncommutative probability space. We also establish
the central limit theorem for half independent
convolution of measures with the limit being
symmetrized Rayleigh. Cramer's theorem is also
established in this set up.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "$C^*$probability space; Central limit theorem;
Cramer's theorem; cumulant; free algebras; free
independence; half commutativity; half independence;
noncommutative probability spaces; Rayleigh
distribution; reverse circulant matrix; semicircular
law",
}
@Article{Abramson:2011:CMR,
author = "Josh Abramson and Jim Pitman and Nathan Ross and
Geronimo Uribe Bravo",
title = "Convex minorants of random walks and {L{\'e}vy}
processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "38:423--38:434",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1648",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1648",
abstract = "This article provides an overview of recent work on
descriptions and properties of the Convex minorants of
random walks and L{\'e}vy processes, which summarize
and extend the literature on these subjects. The
results surveyed include point process descriptions of
the convex minorant of random walks and L{\'e}vy
processes on a fixed finite interval, up to an
independent exponential time, and in the infinite
horizon case. These descriptions follow from the
invariance of these processes under an adequate path
transformation. In the case of Brownian motion, we note
how further special properties of this process,
including time-inversion, imply a sequential
description for the convex minorant of the Brownian
meander.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random walks, L{\'e}vy processes, Brownian meander,
Convex minorant, Uniform stick-breaking, Fluctuation
theory",
}
@Article{Curien:2011:RLM,
author = "Nicolas Curien and Yuval Peres",
title = "Random laminations and multitype branching processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "39:435--39:446",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1641",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1641",
abstract = "We consider multitype branching processes arising in
the study of random laminations of the disk. We
classify these processes according to their subcritical
or supercritical behavior and provide Kolmogorov-type
estimates in the critical case corresponding to the
random recursive lamination process of [1]. The proofs
use the infinite dimensional Perron--Frobenius theory
and quasi-stationary distributions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random trees, random snake",
}
@Article{Liu:2011:EUI,
author = "Wei Liu and Jonas Toelle",
title = "Existence and Uniqueness of Invariant Measures for
Stochastic Evolution Equations with Weakly Dissipative
Drifts",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "40:447--40:457",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1643",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1643",
abstract = "In this paper, a new decay estimate for a class of
stochastic evolution equations with weakly dissipative
drifts is established, which directly implies the
uniqueness of invariant measures for the corresponding
transition semigroups. Moreover, the existence of
invariant measures and the convergence rate of
corresponding transition semigroup to the invariant
measure are also investigated. As applications, the
main results are applied to singular stochastic
$p$-Laplace equations and stochastic fast diffusion
equations, which solves an open problem raised by Barbu
and Da Prato in [Stoc. Proc. Appl. 120(2010),
1247-1266].",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "$p$-Laplace equation; dissipative; fast diffusion
equation; invariant measure; stochastic evolution
equation",
}
@Article{Groeneboom:2011:TMB,
author = "Piet Groeneboom and Nico Temme",
title = "The tail of the maximum of {Brownian} motion minus a
parabola",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "41:458--41:466",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1645",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1645",
abstract = "We analyze the tail behavior of the maximum $N$ of $
\{ W(t) - t^2 : t \ge 0 \} $, where $W$ is standard
Brownian motion on $ [0, \infty)$, and give an
asymptotic expansion for $ {\mathbb P} \{ N \ge x \} $,
as $ x \to \infty $. This extends a first order result
on the tail behavior, which can be deduced from
H{\"u}sler and Piterbarg (1999). We also point out the
relation between certain results in Janson et al.
(2010) and Groeneboom (2010).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion, parabolic drift, maximum, Airy
functions",
}
@Article{Nourdin:2011:YAP,
author = "Ivan Nourdin",
title = "Yet another proof of the {Nualart--Peccati}
criterion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "42:467--42:481",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1642",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1642",
abstract = "In 2005, Nualart and Peccati showed that,
surprisingly, the convergence in distribution of a
normalized sequence of multiple Wiener-It{\^o}
integrals towards a standard Gaussian law is equivalent
to convergence of just the fourth moment to 3.
Recently, this result is extended to a sequence of
multiple Wigner integrals, in the context of free
Brownian motion. The goal of the present paper is to
offer an elementary, unifying proof of these two
results. The only advanced, needed tool is the product
formula for multiple integrals. Apart from this
formula, the rest of the proof only relies on soft
combinatorial arguments.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion; free Brownian motion; multiple
Wiener-It{\^o} integrals; multiple Wigner integrals;
Nualart--Peccati criterion; product formula",
}
@Article{Raimond:2011:IDG,
author = "Olivier Raimond and Bruno Schapira",
title = "Internal {DLA} generated by cookie random walks on
{$Z$}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "43:483--43:490",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1646",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1646",
abstract = "We prove a law of large numbers for the right boundary
in the model of internal DLA generated by cookie random
walks in dimension one. The proof is based on
stochastic recursions techniques.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "excited random walk; Internal DLA; law of large
numbers.",
}
@Article{Hasebe:2011:JCN,
author = "Takahiro Hasebe and Hayato Saigo",
title = "Joint cumulants for natural independence",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "44:491--44:506",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1647",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1647",
abstract = "Many kinds of independence have been defined in
non-commutative probability theory. Natural
independence is an important class of independence;
this class consists of five independences (tensor,
free, Boolean, monotone and anti-monotone ones). In the
present paper, a unified treatment of joint cumulants
is introduced for natural independence. The way we
define joint cumulants enables us not only to find the
monotone joint cumulants but also to give a new
characterization of joint cumulants for other kinds of
natural independence, i.e., tensor, free and Boolean
independences. We also investigate relations between
generating functions of moments and monotone cumulants.
We find a natural extension of the Muraki formula,
which describes the sum of monotone independent random
variables, to the multivariate case.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Natural independence, cumulants, non-commutative
probability, monotone independence",
}
@Article{Gripenberg:2011:WCG,
author = "Gustaf Gripenberg",
title = "White and colored {Gaussian} noises as limits of sums
of random dilations and translations of a single
function",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "45:507--45:516",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1650",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1650",
abstract = "It is shown that a stochastic process obtained by
taking random sums of dilations and translations of a
given function converges to Gaussian white noise if a
dilation parameter grows to infinity and that it
converges to Gaussian colored noise if a scaling
parameter for the translations grows to infinity. In
particular, the question of when one obtains fractional
Brownian motion by integrating this colored noise is
studied.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion; colored noise; convergence; dilation;
fractional Brownian motion; translation; white noise",
}
@Article{Coupier:2011:MGS,
author = "David Coupier",
title = "Multiple geodesics with the same direction",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "46:517--46:527",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1656",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1656",
abstract = "The directed last-passage percolation (LPP) model with
independent exponential times is considered. We
complete the study of asymptotic directions of infinite
geodesics, started by Ferrari and Pimentel [5]. In
particular, using a recent result of [3] and a local
modification argument, we prove there is no (random)
direction with more than two geodesics with probability
1.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "geodesic; last-passage percolation; random tree;
topological end",
}
@Article{Procaccia:2011:GRI,
author = "Eviatar Procaccia and Johan Tykesson",
title = "Geometry of the random interlacement",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "47:528--47:544",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1660",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1660",
abstract = "We consider the geometry of random interlacements on
the $d$-dimensional lattice. We use ideas from
stochastic dimension theory developed in [1] to prove
the following: Given that two vertices $ x, y$ belong
to the interlacement set, it is possible to find a path
between $x$ and $y$ contained in the trace left by at
most $ \lceil d / 2 \rceil $ trajectories from the
underlying Poisson point process. Moreover, this result
is sharp in the sense that there are pairs of points in
the interlacement set which cannot be connected by a
path using the traces of at most $ \lceil d / 2 \rceil
- 1$ trajectories.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random Interlacements; Stochastic dimension",
}
@Article{Bottcher:2011:CFP,
author = "Bj{\"o}rn B{\"o}ttcher",
title = "On the construction of {Feller} processes with
unbounded coefficients",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "48:545--48:555",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1652",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1652",
abstract = "Construction methods for Feller processes which
require bounded coefficients are extended to the case
of unbounded coefficients.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Feller process, Feller semigroup, construction of
Markov processes, unbounded coefficients",
}
@Article{Koudou:2011:WDM,
author = "Angelo Koudou and Pierre Vallois",
title = "Which distributions have the {Matsumoto--Yor}
property?",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "49:556--49:566",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1663",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1663",
abstract = "For four types of functions $ \xi :]0, \infty [\to]0,
\infty [ $, we characterize the law of two independent
and positive r.v.'s $X$ and $Y$ such that $ U := \xi (X
+ Y)$ and $ V := \xi (X) - \xi (X + Y)$ are
independent. The case $ \xi (x) = 1 / x$ has been
treated by Letac and Wesolowski (2000). As for the
three other cases, under the weak assumption that $X$
and $Y$ have density functions whose logarithm is
locally integrable, we prove that the distribution of $
(X, Y)$ is unique. This leads to Kummer, gamma and beta
distributions. This improves the result obtained in [1]
where more regularity was required from the
densities.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Beta distribution.; Gamma distribution; generalized
inverse Gaussian distribution; Kummer distribution;
Matsumoto--Yor property",
}
@Article{Mohle:2011:CPD,
author = "Martin M{\"o}hle",
title = "Coalescent processes derived from some compound
{Poisson} population models",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "50:567--50:582",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1654",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1654",
abstract = "A particular subclass of compound Poisson population
models is analyzed. The models in the domain of
attraction of the Kingman coalescent are characterized
and it is shown that these models are never in the
domain of attraction of any other continuous-time
coalescent process. Results are obtained characterizing
which of these models are in the domain of attraction
of a discrete-time coalescent with simultaneous
multiple mergers of ancestral lineages. The results
extend those obtained by Huillet and the author in
`Population genetics models with skewed fertilities: a
forward and backward analysis', Stochastic Models 27
(2011), 521-554.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Ancestral process; Cannings model; coalescent;
compound Poisson model; conditional branching process
model; Dirichlet model; exchangeability; neutrality;
simultaneous multiple collisions; weak convergence;
Wright--Fisher model",
}
@Article{Kuba:2011:ACC,
author = "Markus Kuba",
title = "Analysis of a class of Cannibal urns",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "51:583--51:599",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1669",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1669",
abstract = "In this note we study a class of $ 2 \times 2 $
Polya-Eggenberger urn models, which serves as a
stochastic model in biology describing cannibalistic
behavior of populations. A special case was studied
before by Pittel using asymptotic approximation
techniques, and more recently by Hwang et al. using
generating functions. We obtain limit laws for the
stated class of so-called cannibal urns by using
Pittel's method, and also different techniques.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Cannibal Urn models, Normal distribution, Poisson
distribution",
}
@Article{Ma:2011:TII,
author = "Yutao Ma and Ran Wang and Liming Wu",
title = "Transportation-information inequalities for continuum
{Gibbs} measures",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "52:600--52:613",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1670",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1670",
abstract = "The objective of this paper is to establish explicit
concentration inequalities for the Glauber dynamics
related with continuum or discrete Gibbs measures. At
first we establish the optimal
transportation-information $ W_1 I$-inequality for the
$ M / M / \infty $-queue associated with the Poisson
measure, which improves several previous known results.
Under the Dobrushin's uniqueness condition, we obtain
some explicit $ W_1 I$-inequalities for Gibbs measures
both in the continuum and in the discrete lattice. Our
method is a combination of Lipschitzian spectral gap,
the Lyapunov test function approach and the
tensorization technique.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "transportation-information inequality, concentration
inequality, Gibbs measure, Lyapunov function method",
}
@Article{Sayit:2011:AFM,
author = "Hasanjan Sayit and Frederi Viens",
title = "Arbitrage-free Models In Markets With Transaction
Costs",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "53:614--53:622",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1671",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1671",
abstract = "In the paper [7], Guasoni studies financial markets
which are subject to proportional transaction costs.
The standard martingale framework of stochastic finance
is not applicable in these markets, since the
transaction costs force trading strategies to have
bounded variation, while continuous- time martingale
strategies have infinite transaction cost. The main
question that arises out of [7] is whether it is
possible to give a convenient condition to guarantee
that a trading strategy has no arbitrage. Such a
condition was proposed and studied in [6] and [1], the
so-called stickiness property, whereby an asset's price
is never certain to exit a ball within a predetermined
finite time. In this paper, we define the
multidimensional extension of the stickiness property,
to handle arbitrage-free conditions for markets with
multiple assets and proportional transaction costs. We
show that this condition is sufficient for a
multi-asset model to be free of arbitrage. We also show
that d-dimensional fractional Brownian models are
jointly sticky, and we establish a time-change result
for joint stickiness.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Financial markets, arbitrage, transaction cost, sticky
process, fractional Brownian motion, time-change",
}
@Article{Simon:2011:MSP,
author = "Thomas Simon",
title = "A multiplicative short proof for the unimodality of
stable densities",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "54:623--54:629",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1672",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1672",
abstract = "Revisiting an article by Chernin and Ibragimov on
unimodality of stable laws, we show that their approach
to deduce the general case from the extremal ones,
whose completion contained an error as discovered later
by Kanter, can be carried out successfully in
considering Bochner's subordination and multiplicative
strong unimodality. This short proof of the unimodality
of all stable densities yields also a multiplicative
counterpart to Yamazato's additive ones.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stable law; unimodality",
}
@Article{Bergqvist:2011:RPR,
author = "G{\"o}ran Bergqvist and Peter Forrester",
title = "Rank probabilities for real random {$ N \times N
\times 2 $} tensors",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "55:630--55:637",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1655",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1655",
abstract = "We prove that the probability $ P_N $ for a real
random Gaussian $ N \times N \times 2 $ tensor to be of
real rank $N$ is $ P_N = (\Gamma ((N + 1) / 2))^N / G(N
+ 1)$, where $ \Gamma (x)$, $ G(x)$ denote the gamma
and Barnes $G$-functions respectively. This is a
rational number for $N$ odd and a rational number
multiplied by $ \pi^{N / 2}$ for $N$ even. The
probability to be of rank $ N + 1$ is $ 1 - P_N$. The
proof makes use of recent results on the probability of
having $k$ real generalized eigenvalues for real random
Gaussian $ N \times N$ matrices. We also prove that $
\log P_N = (N^2 / 4) \log (e / 4) + (\log N - 1) / 12 -
\zeta '( - 1) + {\rm O}(1 / N)$ for large $N$, where $
\zeta $ is the Riemann zeta function.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "multi-way arrays; random matrices; tensors; typical
rank",
}
@Article{Jones:2011:CHT,
author = "Owen Jones and David Rolls",
title = "A characterisation of, and hypothesis test for,
continuous local martingales",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "56:638--56:651",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1673",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1673",
abstract = "We give characterisations for Brownian motion and
continuous local martingales, using the crossing tree,
which is a sample-path decomposition based on
first-passages at nested scales. These results are
based on ideas used in the construction of Brownian
motion on the Sierpinski gasket (Barlow and Perkins
1988). Using our characterisation we propose a test for
the continuous martingale hypothesis, that is, that a
given process is a continuous local martingale. The
crossing tree gives a natural break-down of a sample
path at different spatial scales, which we use to
investigate the scale at which a process looks like a
continuous local martingale. Simulation experiments
indicate that our test is more powerful than an
alternative approach which uses the sample quadratic
variation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "continuous martingale hypothesis; crossing-tree;
realised volatility; time-change",
}
@Article{Markowsky:2011:EET,
author = "Greg Markowsky",
title = "On the expected exit time of planar {Brownian} motion
from simply connected domains",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "57:652--57:663",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1653",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1653",
abstract = "In this note, we explore applications of a known lemma
which relates the expected exit time of Brownian motion
from a simply connected domain with the power series of
a conformal map into that domain. We use the lemma to
calculate the expected exit time from a number of
domains, and in the process describe a probabilistic
method for summing certain series. In particular, we
give a proof of Euler's classical result that $ \zeta
(2) = \pi^2 / 6 $. We also show how the relationship
between the power series and the Brownian exit time
gives several immediate consequences when teamed with a
deep result of de Branges concerning the coefficients
of power series of normalized conformal maps. We
conclude by stating an extension of the lemma in
question to domains which are not simply connected.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion; conformal maps; exit time",
}
@Article{Karatzas:2011:OST,
author = "Ioannis Karatzas and Albert Shiryaev and Mykhaylo
Shkolnikov",
title = "On the one-sided {Tanaka} equation with drift",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "58:664--58:677",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1665",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1665",
abstract = "We study questions of existence and uniqueness of weak
and strong solutions for a one-sided Tanaka equation
with constant drift lambda. We observe a dichotomy in
terms of the values of the drift parameter: for $
\lambda \leq 0 $, there exists a strong solution which
is pathwise unique, thus also unique in distribution;
whereas for $ \lambda > 0 $, the equation has a unique
in distribution weak solution, but no strong solution
(and not even a weak solution that spends zero time at
the origin). We also show that strength and pathwise
uniqueness are restored to the equation via suitable
``Brownian perturbations''.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stochastic differential equation, weak existence, weak
uniqueness, strong existence, strong uniqueness, Tanaka
equation, skew Brownian motion, sticky Brownian motion,
comparison theorems for diffusions",
}
@Article{Dong:2011:IMS,
author = "Zhao Dong and Lihu Xu and Xicheng Zhang",
title = "Invariant measures of stochastic {$ 2 D $}
{Navier--Stokes} equation driven by $ \alpha $-stable
processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "59:678--59:688",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1664",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1664",
abstract = "In this note we prove the well-posedness for
stochastic $ 2 D $ Navier--Stokes equation driven by
general L{\'e}vy processes (in particular, $ \alpha
$-stable processes), and obtain the existence of
invariant measures.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "$alpha$-stable process, Stochastic Navier--Stokes
equation, Invariant measure",
}
@Article{VanNeerven:2011:MIS,
author = "Jan {Van Neerven} and Jiahui Zhu",
title = "A maximal inequality for stochastic convolutions in
$2$-smooth {Banach} spaces",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "60:689--60:705",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1677",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1677",
abstract = "Let $ (e^{tA})_{t \geq 0} $ be a $ C_0$-contraction
semigroup on a $2$-smooth Banach space $E$, let $
(W_t)_{t \geq 0}$ be a cylindrical Brownian motion in a
Hilbert space $H$, and let $ (g_t)_{t \geq 0}$ be a
progressively measurable process with values in the
space $ \gamma (H, E)$ of all $ \gamma $-Radonifying
operators from $H$ to $E$. We prove that for all $ 0 <
p < \infty $ there exists a constant $C$, depending
only on $p$ and $E$, such that for all $ T \geq 0$ we
have\par
$$ E \sup_{0 \leq t \leq T} \left \Vert \int_0^t \!
e^{(t - s)A} \, g_s d W_s \right \Vert^p \leq C E \left
(\int_0^T \! \left (\left \Vert g_t \right
\Vert_{\gamma (H, E)} \right)^2 \, d t \right)^{p / 2}.
$$
For $ p \geq 2$ the proof is based on the observation
that $ \psi (x) = \Vert x \Vert^p$ is Fr{\'e}chet
differentiable and its derivative satisfies the
Lipschitz estimate $ \Vert \psi '(x) - \psi '(y) \Vert
\leq C \left (\Vert x \Vert + \Vert y \Vert \right)^{p
- 2} \Vert x - y \Vert $; the extension to $ 0 < p < 2$
proceeds via Lenglart's inequality.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stochastic convolutions, maximal inequality,
$2$-smooth Banach spaces, It{\^o} formula.",
}
@Article{Sen:2011:ACL,
author = "Arnab Sen and Balint Virag",
title = "Absolute continuity of the limiting eigenvalue
distribution of the random {Toeplitz} matrix",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "61:706--61:711",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1675",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1675",
abstract = "We show that the limiting eigenvalue distribution of
random symmetric Toeplitz matrices is absolutely
continuous with density bounded by 8, partially
answering a question of Bryc, Dembo and Jiang (2006).
The main tool used in the proof is a spectral averaging
technique from the theory of random Schr{\"o}dinger
operators. The similar question for Hankel matrices
remains open",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Toeplitz matrix, eigenvalue distribution, spectral
averaging",
}
@Article{Quastel:2011:LBP,
author = "Jeremy Quastel and Daniel Remenik",
title = "Local {Brownian} property of the narrow wedge solution
of the {KPZ} equation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "62:712--62:719",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1678",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1678",
abstract = "Abstract. Let $ H(t, x) $ be the Hopf-Cole solution at
time t of the Kardar--Parisi--Zhang (KPZ) equation
starting with narrow wedge initial condition, i.e. the
logarithm of the solution of the multiplicative
stochastic heat equation starting from a Dirac delta.
Also let $ H^{eq}(t, x) $ be the solution at time $t$
of the KPZ equation with the same noise, but with
initial condition given by a standard two-sided
Brownian motion, so that $ H^{eq}(t, x) - H^{eq}(0, x)$
is itself distributed as a standard two-sided Brownian
motion. We provide a simple proof of the following
fact: for fixed $t$, $ H(t, x) - (H^{eq}(t, x) -
H^{eq}(t, 0))$ is locally of finite variation. Using
the same ideas we also show that if the KPZ equation is
started with a two-sided Brownian motion plus a
Lipschitz function then the solution stays in this
class for all time.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "asymmetric exclusion process; Brownian motion;
directed polymers; finite variation;
Kardar--Parisi--Zhang equation; random growth;
stochastic Burgers equation; stochastic heat equation",
}
@Article{Pardoux:2011:BML,
author = "Etienne Pardoux and Anton Wakolbinger",
title = "From {Brownian} motion with a local time drift to
{Feller}'s branching diffusion with logistic growth",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "63:720--63:731",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1679",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1679",
abstract = "We give a new proof for a Ray-Knight representation of
Feller's branching diffusion with logistic growth in
terms of the local times of a reflected Brownian motion
$H$ with a drift that is affine linear in the local
time accumulated by $H$ at its current level. In Le et
al. (2011) such a representation was obtained by an
approximation through Harris paths that code the
genealogies of particle systems. The present proof is
purely in terms of stochastic analysis, and is inspired
by previous work of Norris, Rogers and Williams
(1988).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Ray-Knight representation, local time, Feller
branching with logistic growth, Brownian motion, local
time drift, Girsanov transform",
}
@Article{Fernandez:2011:RMA,
author = "Roberto Fernandez and Sandro Gallo and Gregory
Maillard",
title = "Regular $g$-measures are not always {Gibbsian}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "64:732--64:740",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1681",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1681",
abstract = "Regular g-measures are discrete-time processes
determined by conditional expectations with respect to
the past. One-dimensional Gibbs measures, on the other
hand, are fields determined by simultaneous
conditioning on past and future. For the Markovian and
exponentially continuous cases both theories are known
to be equivalent. Its equivalence for more general
cases was an open problem. We present a simple example
settling this issue in a negative way: there exist
$g$-measures that are continuous and non-null but are
not Gibbsian. Our example belongs, in fact, to a
well-studied family of processes with rather nice
attributes: It is a chain with variable-length memory,
characterized by the absence of phase coexistence and
the existence of a visible renewal scheme",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Discrete-time stochastic processes, $g$-measures,
chains with complete connections, non-Gibbsianness,
chains with variable-length memory",
}
@Article{Ramirez:2011:HET,
author = "Jose Ramirez and Brian Rider and Ofer Zeitouni",
title = "Hard edge tail asymptotics",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "65:741--65:752",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1682",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1682",
abstract = "Let $ \Lambda $ be the limiting smallest eigenvalue in
the general $ (\beta, a)$-Laguerre ensemble of random
matrix theory. That is, $ \Lambda $ is the $ n \to
\infty $ distributional limit of the (scaled) minimal
point drawn from the density proportional to $ \Pi_1
\leq i \leq j \leq n$ \par
$$ \left | \lambda_i - \lambda_j \right |^\beta
\prod_{i = 1}^n \lambda_i^{\frac {\beta }{2}(a + 1) -
1}e^{- \frac {\beta }{2} \lambda_i} $$
on $ (\mathbb {R}_+^n$. Here $ \beta > 0$, $ a > - 1$;
for $ \beta = 1, 2, 4$ and integer $a$, this object
governs the singular values of certain rank $n$
Gaussian matrices. We prove that\par
$$ \mathbb {P}(\Lambda > \lambda) = e^{- \frac {\beta
}{2} \lambda + 2 \gamma \sqrt {\lambda }} \lambda^{-
\frac {\gamma (\gamma + 1 - \beta / 2)}{2 \beta }}
e(\beta, a)(1 + o(1)) $$
as $ \lambda \to \infty $ in which\par
$$ \gamma = \frac {\beta }{2} (a + 1) - 1 $$
and $ e(\beta, a) > 0$ is a constant (which we do not
determine). This estimate complements/extends various
results previously available for special values of $
\beta $ and $a$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random matrices, smallest singular value, hard edge",
}
@Article{Merkl:2011:CIE,
author = "Franz Merkl and Silke Rolles",
title = "Correlation Inequalities for Edge-Reinforced Random
Walk",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "66:753--66:763",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1683",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1683",
abstract = "We prove correlation inequalities for linearly
edge-reinforced random walk. These correlation
inequalities concern the first entry tree, i.e. the
tree of edges used to enter any vertex for the first
time. They also involve the asymptotic fraction of time
spent on particular edges. Basic ingredients are known
FKG-type inequalities and known negative associations
for determinantal processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "FKG inequalities; reinforced random walk; spanning
trees",
}
@Article{Lejay:2011:SSP,
author = "Antoine Lejay",
title = "Simulation of a stochastic process in a discontinuous
layered medium",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "67:764--67:774",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1686",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1686",
abstract = "In this note, we provide a simulation algorithm for a
diffusion process in a layered media. Our main tools
are the properties of the Skew Brownian motion and a
path decomposition technique for simulating occupation
times.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Skew Brownian motion, discontinuous media, occupation
time, local time, last passage time, path
decomposition, Brownian bridge, first hitting time,
geophysics, Monte Carlo simulation",
}
@Article{Sapozhnikov:2011:IIC,
author = "Artem Sapozhnikov",
title = "The incipient infinite cluster does not stochastically
dominate the invasion percolation cluster in two
dimensions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "68:775--68:780",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1684",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1684",
abstract = "This note is motivated by results of Angel, Goodman,
den Hollander and Slade (2008) and Damron, Sapozhnikov
and Vagvolgyi (2009) about global relations between the
invasion percolation cluster (IPC) and the incipient
infinite cluster (IIC) on regular trees and on two
dimensional lattices, respectively. Namely, that the
laws of the two objects are mutually singular, and, in
the case of regular trees, that the IIC stochastically
dominates the IPC. We prove that on two dimensional
lattices, the IIC does not stochastically dominate the
IPC. This is the first example showing that the
relation between the IIC and IPC is significantly
different on trees and in two dimensions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Invasion percolation, incipient infinite cluster,
critical percolation, near-critical percolation,
correlation length, stochastic domination.",
}
@Article{Hutzenthaler:2011:SBD,
author = "Martin Hutzenthaler",
title = "Supercritical branching diffusions in random
environment",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "69:781--69:791",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1685",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1685",
abstract = "Supercritical branching processes in constant
environment conditioned on eventual extinction are
known to be subcritical branching processes. The case
of random environment is more subtle. A supercritical
branching diffusion in random environment (BDRE)
conditioned on eventual extinction of the population is
not a branching diffusion in a homogeneous environment.
However the law of the population size of a
supercritical BDRE (averaged over the environment)
conditioned on eventual extinction is equal to the law
of the population size of a subcritical BDRE (averaged
over the environment). As a consequence, supercritical
BDREs have a phase transition which is similar to a
well-known phase transition of subcritical branching
processes in random environment.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Branching diffusions in random environment, BDRE,
supercriticality, survival probability",
}
@Article{Athreya:2011:ODV,
author = "Siva Athreya and Rongfeng Sun",
title = "One-dimensional Voter Model Interface Revisited",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "16",
pages = "70:792--70:800",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v16-1688",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1688",
abstract = "We consider the voter model on $ \mathbb {Z} $,
starting with all 1's to the left of the origin and all
$0$'s to the right of the origin. It is known that if
the associated random walk kernel $p$ has zero mean and
a finite r-th moment for any $ r > 3$, then the
evolution of the boundaries of the interface region
between 1's and 0's converge in distribution to a
standard Brownian motion $ (B_t)_{t > 0}$ under
diffusive scaling of space and time. This convergence
fails when $p$ has an infinite $r$-th moment for any $
r < 3$, due to the loss of tightness caused by a few
isolated $1$'s appearing deep within the regions of all
$0$'s (and vice versa) at exceptional times. In this
note, we show that as long as $p$ has a finite second
moment, the measure-valued process induced by the
rescaled voter model configuration is tight, and
converges weakly to the measure-valued process $ 1_{x <
B_t} d x$, $ t > 0$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "voter model interface, measure-valued process,
tightness",
}
@Article{Benjamini:2012:RVI,
author = "Itai Benjamini and Nicolas Curien",
title = "Recurrence of the $ \mathbb {Z}^d$-valued infinite
snake via unimodularity",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "1:1--1:10",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1700",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1700",
abstract = "We use the concept of unimodular random graph to show
that the branching simple random walk on $ \mathbb
{Z}^d $ indexed by a critical geometric Galton--Watson
tree conditioned to survive is recurrent if and only if
$ d \leq 4 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Galton--Watson trees; random snake; recurrence",
}
@Article{vandenBerg:2012:PPB,
author = "Jacob van den Berg and Demeter Kiss and Pierre Nolin",
title = "A percolation process on the binary tree where large
finite clusters are frozen",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "2:1--2:11",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1694",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1694",
abstract = "We study a percolation process on the planted binary
tree, where clusters freeze as soon as they become
larger than some fixed parameter N. We show that as N
goes to infinity, the process converges in some sense
to the frozen percolation process introduced by Aldous.
In particular, our results show that the asymptotic
behaviour differs substantially from that on the square
lattice, on which a similar process has been studied
recently by van den Berg, de Lima and Nolin.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "frozen cluster; percolation",
}
@Article{Freund:2012:ASA,
author = "Fabian Freund",
title = "Almost sure asymptotics for the number of types for
simple {$ \Xi $}-coalescents",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "3:1--3:11",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1704",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1704",
abstract = "Let $ K_n $ be the number of types in the sample $
\left \{ 1, \ldots, n \right \} $ of a $ \Xi
$-coalescent $ \Pi = (\Pi_t)_{t \geq 0}$ with mutation
and mutation rate $ r > 0$. Let $ \Pi^{(n)}$ be the
restriction of $ \Pi $ to the sample. It is shown that
$ M_n / n$, the fraction of external branches of $
\Pi^{(n)}$ which are affected by at least one mutation,
converges almost surely and in $ L^p$ ($ p \geq 1$) to
$ M := \int^{\infty }_0 r e^{-rt}S_t d t$, where $ S_t$
is the fraction of singleton blocks of $ \Pi_t$. Since
for coalescents without proper frequencies, the effects
of mutations on non-external branches is neglectible
for the asymptotics of $ K_n / n$, it is shown that $
K_n / n \rightarrow M$ for $ n \rightarrow \infty $ in
$ L^p$ $ (p \geq 1)$. For simple coalescents, this
convergence is shown to hold almost surely. The almost
sure results are based on a combination of the Kingman
correspondence for random partitions and strong laws of
large numbers for weighted i.i.d. or exchangeable
random variables.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "almost sure convergence; coalescent; external
branches; mutation",
}
@Article{Hillion:2012:CEA,
author = "Erwan Hillion",
title = "Concavity of entropy along binomial convolutions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "4:1--4:9",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1707",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1707",
abstract = "Motivated by a generalization of Sturm-Lott-Villani
theory to discrete spaces and by a conjecture stated by
Shepp and Olkin about the entropy of sums of Bernoulli
random variables, we prove the concavity in $t$ of the
entropy of the convolution of a probability measure
$a$, which has the law of a sum of independent
Bernoulli variables, by the binomial measure of
parameters $ n \geq 1$ and $t$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "binomial distribution; concavity of entropy;
Olkin-Shepp conjecture",
}
@Article{Goldberg:2012:CRM,
author = "Leslie Goldberg and Mark Jerrum",
title = "A counterexample to rapid mixing of the
{Ge--Stefankovic} process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "5:1--5:6",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1712",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1712",
abstract = "Ge and Stefankovic have recently introduced a Markov
chain which, if rapidly mixing, would provide an
efficient procedure for sampling independent sets in a
bipartite graph. Such a procedure would be a
breakthrough because it would give an efficient
randomised algorithm for approximately counting
independent sets in a bipartite graph, which would in
turn imply the existence of efficient approximation
algorithms for a number of significant counting
problems whose computational complexity is so far
unresolved. Their Markov chain is based on a novel
two-variable graph polynomial which, when specialised
to a bipartite graph, and evaluated at the point (1/2,
1), gives the number of independent sets in the graph.
The Markov chain is promising, in the sense that it
overcomes the most obvious barrier to rapid mixing.
However, we show here, by exhibiting a sequence of
counterexamples, that its mixing timeis exponential in
the size of the input when the input is chosen from a
particular infinite family of bipartite graphs.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Glauber dynamics; Independent sets in graphs; Markov
chains; Mixing time; Randomised algorithms",
}
@Article{Denisov:2012:MAS,
author = "Denis Denisov and Vitali Wachtel",
title = "Martingale approach to subexponential asymptotics for
random walks",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "6:1--6:9",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1757",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1757",
abstract = "Consider the random walk $ S_n = \xi_1 + \cdots +
\xi_n $ with independent and identically distributed
increments and negative mean $ \mathbf E \xi = - m < 0
$. Let $ M = \sup_{0 \le i} S_i $ be the supremum of
the random walk. In this note we present derivation of
asymptotics for $ \mathbf P(M > x), x \to \infty $ for
long-tailed distributions. This derivation is based on
the martingale arguments and does not require any prior
knowledge of the theory of long-tailed distributions.
In addition the same approach allows to obtain
asymptotics for $ \mathbf P(M_\tau > x) $, where $
M_\tau = \max_{0 \le i < \tau }S_i $ and $ \tau = \min
\{ n \ge 1 : S_n \le 0 \} $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "cycle maximum; heavy-tailed distribution; random walk;
stopping time; supremum",
}
@Article{Cator:2012:IIC,
author = "Eric Cator and Leandro Pimentel and Marcio Souza",
title = "Influence of the initial condition in equilibrium
last-passage percolation models",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "7:1--7:7",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1727",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1727",
abstract = "In this paper we consider an equilibrium last-passage
percolation model on an environment given by a compound
two-dimensional Poisson process. We prove an $ \mathbb
{L}^2$-formula relating the initial measure with the
last-passage percolation time. This formula turns out
to be a useful tool to analyze the fluctuations of the
last-passage times along non-characteristic
directions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Equilibrium measure; Hammersley process; Interacting
particle system; Last passage percolation",
}
@Article{Mueller:2012:ECB,
author = "Carl Mueller and Zhixin Wu",
title = "Erratum: {``A connection between the stochastic heat
equation and fractional Brownian motion, and a simple
proof of a result of Talagrand''}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "8:1--8:10",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1774",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See \cite{Mueller:2009:CBS}.",
URL = "http://ecp.ejpecp.org/article/view/1774",
abstract = "We give a new representation of fractional Brownian
motion with Hurst parameter $ H < 1 / 2 $ using
stochastic partial differential equations. This
representation allows us to use the Markov property and
time reversal, tools which are not usually available
for fractional Brownian motion. We then give simple
proofs that fractional Brownian motion does not hit
points in the critical dimension, and that it does not
have double points in the critical dimension. These
facts were already known, but our proofs are quite
simple and use some ideas of L{\'e}vy. This is an
Erratum for
\url{https://doi.org/10.1214/ECP.v14-1403}ECP volume 14
paper number 6.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "heat equation; stochastic partial differential
equations; white noise",
}
@Article{Sznitman:2012:ITR,
author = "Alain-Sol Sznitman",
title = "An isomorphism theorem for random interlacements",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "9:1--9:9",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1792",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1792",
abstract = "We consider continuous-time random interlacements on a
transient weighted graph. We prove an identity in law
relating the field of occupation times of random
interlacements at level u to the Gaussian free field on
the weighted graph. This identity is closely linked to
the generalized second Ray-Knight theorem, and uniquely
determines the law of occupation times of random
interlacements at level u.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "random interlacements, Gaussian free field,
isomorphism theorem, generalized second Ray-Knight
theorem.",
}
@Article{Konig:2012:LDL,
author = "Wolfgang K{\"o}nig and Michele Salvi and Tilman
Wolff",
title = "Large deviations for the local times of a random walk
among random conductances",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "10:1--10:11",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1820",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1820",
abstract = "We derive an annealed large deviation principle for
the normalised local times of a continuous-time random
walk among random conductances in a finite domain in $
\mathbb {Z}^d $ in the spirit of Donsker-Varadhan
[DV75-83]. We work in the interesting case that the
conductances may assume arbitrarily small values. Thus,
the underlying picture of the principle is a joint
strategy of small values of the conductances and large
holding times of the walk. The speed and the rate
function of our principle are explicit in terms of the
lower tails of the conductance distribution. As an
application, we identify the logarithmic asymptotics of
the lower tails of the principal eigenvalue of the
randomized negative Laplace operator in the domain.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "continuous-time random walk; Donsker-Varadhan rate
function; large deviations; random conductances;
randomized Laplace operator",
}
@Article{Arizmendi:2012:PFR,
author = "Octavio Arizmendi and Carlos Vargas",
title = "Products of free random variables and $k$-divisible
non-crossing partitions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "11:1--11:13",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1773",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1773",
abstract = "We derive a formula for the moments and the free
cumulants of the multiplication of $k$ free random
variables in terms of $k$-equal and $k$-divisible
non-crossing partitions. This leads to a new simple
proof for the bounds of the right-edge of the support
of the free multiplicative convolution $ \mu^{\boxtimes
k}$, given by Kargin, which show that the support grows
at most linearly with $k$. Moreover, this combinatorial
approach generalize the results of Kargin since we do
not require the convolved measures to be identical. We
also give further applications, such as a new proof of
the limit theorem of Sakuma and Yoshida.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Free multiplicative convolution; Free Probability;
Non-crossing partitions",
}
@Article{Goreac:2012:NLM,
author = "Dan Goreac and Oana Silvia Serea",
title = "A note on linearization methods and dynamic
programming principles for stochastic discontinuous
control problems",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "12:1--12:12",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1844",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1844",
abstract = "Using the linear programming approach to stochastic
control introduced by Buckdahn, Goreac, and
Quincampoix, and by Goreac and Serea, we provide a
semigroup property for some set of probability measures
leading to dynamic programming principles for
stochastic control problems. An abstract principle is
provided for general bounded costs. Linearized versions
are obtained under further (semi)continuity
assumptions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "dynamic programming principles; occupational measures;
stochastic control",
}
@Article{Ejsmont:2012:LLP,
author = "Wiktor Ejsmont",
title = "{Laha--Lukacs} properties of some free processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "13:1--13:8",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1865",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1865",
abstract = "We study the Laha--Lukacs property of the free Meixner
laws (processes). We prove that some families of free
Meixner distribution have the linear regression
function. We also show that this families have the
property of quadratic conditional variances.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "conditional expectation; free cumulants; Free Meixner
law; Laha--Lukacs theorem; noncommutative quadratic
regression; von Neumann algebras.",
}
@Article{Hsu:2012:TIS,
author = "Daniel Hsu and Sham Kakade and Tong Zhang",
title = "Tail inequalities for sums of random matrices that
depend on the intrinsic dimension",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "14:1--14:13",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1869",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1869",
abstract = "This work provides exponential tail inequalities for
sums of random matrices that depend only on intrinsic
dimensions rather than explicit matrix dimensions.
These tail inequalities are similar to the matrix
versions of the Chernoff bound and Bernstein inequality
except with the explicit matrix dimensions replaced by
a trace quantity that can be small even when the
explicit dimensions are large or infinite. Some
applications to covariance estimation and approximate
matrix multiplication are given to illustrate the
utility of the new bounds.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Cammarota:2012:MVS,
author = "Valentina Cammarota and Peter M{\"o}rters",
title = "On the most visited sites of planar {Brownian}
motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "15:1--15:9",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1809",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1809",
abstract = "Let $ (B_t \colon t \ge 0) $ be a planar Brownian
motion and define gauge functions $ \phi_\alpha (s) =
\log (1 / s)^{- \alpha } $ for $ \alpha > 0 $. If $
\alpha < 1 $ we show that almost surely there exists a
point $x$ in the plane such that $ {\mathcal
H}^{\phi_\alpha }(\{ t \ge 0 \colon B_t = x \}) > 0$,
but if $ \alpha > 1$ almost surely $ {\mathcal
H}^{\phi_\alpha } (\{ t \ge 0 \colon B_t = x \}) = 0$
simultaneously for all $ x \in {\mathbb R}^2$. This
resolves a longstanding open problem posed by S. J.
Taylor in 1986.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion, Hausdorff dimension, Hausdorff gauge,
local time, point of infinite multiplicity, uniform
dimension estimates.",
}
@Article{Zhao:2012:UAE,
author = "James Zhao",
title = "Universality of asymptotically {Ewens} measures on
partitions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "16:1--16:11",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1956",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1956",
abstract = "We give a criterion for functionals of partitions to
converge to a universal limit under a class of measures
that {"behaves} {like"} the Ewens measure. Various
limit theorems for the Ewens measure, most notably the
Poisson--Dirichlet limit for the longest parts, the
functional central limit theorem for the number of
parts, and the Erdos-Turan limit for the product of
parts, extend to these asymptotically Ewens measures as
easy corollaries. Our major contributions are: (1)
extending the classes of measures for which these limit
theorems hold; (2) characterising universality by an
intuitive and easily-checked criterion; and (3)
providing a new and much shorter proof of the limit
theorems by taking advantage of the Feller coupling.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "central limit theorem; Erdos-Turan theorem; Ewens
sampling formula; Feller coupling; logarithmic
combinatorial structures; perturbation;
Poisson--Dirichlet limit",
}
@Article{Klimovsky:2012:HDG,
author = "Anton Klimovsky",
title = "High-dimensional {Gaussian} fields with isotropic
increments seen through spin glasses",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "17:1--17:14",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1994",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1994",
abstract = "We study the free energy of a particle in (arbitrary)
high-dimensional Gaussian random potentials with
isotropic increments. We prove a computable saddle
point variational representation in terms of a
Parisi-type functional for the free energy in the
infinite-dimensional limit. The proofs are based on the
techniques developed in the course of the rigorous
analysis of the Sherrington-Kirkpatrick model with
vector spins.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Gaussian random fields; hierarchical replica symmetry
breaking; isotropic increments; Parisi Ansatz; random
energy model",
}
@Article{Benjamini:2012:EMA,
author = "Itai Benjamini and Ariel Yadin and Ofer Zeitouni",
title = "Erratum: {Maximal arithmetic progressions in random
subsets}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "18:1--18:1",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2014",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See \cite{Benjamini:2007:MAP}.",
URL = "http://ecp.ejpecp.org/article/view/2014",
abstract = "{\bf This is an erratum for ``Maximal arithmetic
progressions in random subsets'', which appeared in
\url{https://doi.org/10.1214/ECP.v12-1321} ECP volume
{\bf 12} paper number 35 (2007), 365--376.}",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Hardy:2012:NLD,
author = "Adrien Hardy",
title = "A note on large deviations for {$2$D} {Coulomb} gas
with weakly confining potential",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "19:1--19:12",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1818",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1818",
abstract = "We investigate a Coulomb gas in a potential satisfying
a weaker growth assumption than usual and establish a
large deviation principle for its empirical measure. As
a consequence the empirical measure is seen to converge
towards a non-random limiting measure, characterized by
a variational principle from logarithmic potential
theory, which may not have compact support. The proof
of the large deviation upper bound is based on a
compactification procedure which may be of help for
further large deviation principles.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Compactification; Coulomb gas; Large deviations;
Random matrices",
}
@Article{Maples:2012:NCR,
author = "Kenneth Maples and Ashkan Nikeghbali and Dirk
Zeindler",
title = "On the number of cycles in a random permutation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "20:1--20:13",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1934",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1934",
abstract = "We show that the number of cycles in a random
permutation chosen according to generalized Ewens
measure is normally distributed and compute asymptotic
estimates for the mean and variance.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "random permutation, generalized Ewens measure, total
number of cycles, central limit theorem, large
deviations",
}
@Article{Bobkov:2012:BCF,
author = "Sergey Bobkov and Gennadiy Chistyakov and Friedrich
G{\"o}tze",
title = "Bounds for characteristic functions in terms of
quantiles and entropy",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "21:1--21:9",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2053",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2053",
abstract = "Upper bounds on characteristic functions are derived
in terms of the entropic distance to the class of
normal distributions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Characteristic functions; entropy; quantiles",
}
@Article{Schapira:2012:LVR,
author = "Bruno Schapira",
title = "A $0$-$1$ law for vertex-reinforced random walks on $
\mathbb {Z}$ with weight of order $ k^\alpha $, $
\alpha \in [0, 1 / 2)$",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "22:1--22:8",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2084",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2084",
abstract = "We prove that Vertex Reinforced Random Walk on $
\mathbb {Z} $ with weight of order $ k^\alpha $, with $
\alpha \in [0, 1 / 2) $, is either almost surely
recurrent or almost surely transient. This improves a
previous result of Volkov who showed that the set of
sites which are visited infinitely often was a.s.
either empty or infinite.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "$0$-$1$ law; Reinforced random walk; Self-interacting
random walk",
}
@Article{Vakeroudis:2012:SID,
author = "Stavros Vakeroudis and Marc Yor",
title = "Some infinite divisibility properties of the
reciprocal of planar {Brownian} motion exit time from a
cone",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "23:1--23:9",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2090",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2090",
abstract = "With the help of the Gauss-Laplace transform for the
exit time from a cone of planar Brownian motion, we
obtain some infinite divisibility properties for the
reciprocal of this exit time.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bougerol's identity; Chebyshev polynomials;
generalized Gamma convolution (GGC); infinite
divisibility; L\'\{e\}vy measure; Thorin measure",
}
@Article{Nutz:2012:PCS,
author = "Marcel Nutz",
title = "Pathwise construction of stochastic integrals",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "24:1--24:7",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2099",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2099",
abstract = "We propose a method to construct the stochastic
integral simultaneously under a non-dominated family of
probability measures. Path-by-path, and without
referring to a probability measure, we construct a
sequence of Lebesgue-Stieltjes integrals whose medial
limit coincides with the usual stochastic integral
under essentially any probability measure such that the
integrator is a semimartingale. This method applies to
any predictable integrand.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "aggregation; G-expectation; medial limit;
non-dominated model; Pathwise stochastic integral;
second order BSDE",
}
@Article{Delattre:2012:TFS,
author = "Sylvain Delattre and Mathieu Rosenbaum",
title = "Testing the finiteness of the support of a
distribution: a statistical look at {Tsirelson}'s
equation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "25:1--25:7",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1834",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1834",
abstract = "We consider the following statistical problem: based
on an i.i.d. sample of size $n$ of integer valued
random variables with common law $ \mu $, is it
possible to test whether or not the support of $ \mu $
is finite as $n$ goes to infinity? This question is in
particular connected to a simple case of Tsirelson's
equation, for which it is natural to distinguish
between two main configurations, the first one leading
only to laws with finite support, and the second one
including laws with infinite support. We show that it
is in fact not possible to discriminate between the two
situations, even using a very weak notion of
statistical test.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Hypothesis testing; Tsirelson's equation",
}
@Article{Gnedin:2012:EUI,
author = "Alexander Gnedin and Alexander Marynych",
title = "Exponential--uniform identities related to records",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "26:1--26:5",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2011",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2011",
abstract = "Symmetry properties of the random grid spanned on the
set of records from the planar Poisson point process
imply bizarre multivariate distributional identities
for certain rational functions of independent
exponential and uniform random variables.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "distributional identities; planar Poisson process;
records",
}
@Article{Cranston:2012:CIS,
author = "Michael Cranston and Stanislav Molchanov",
title = "On a concentration inequality for sums of independent
isotropic vectors",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "27:1--27:8",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2063",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2063",
abstract = "We consider a version of a classical concentration
inequality for sums of independent, isotropic random
vectors with a mild restriction on the distribution of
the radial part of these vectors. The proof uses a
little Fourier analysis, the Laplace asymptotic method
and a conditioning idea that traces its roots to some
of the original works on concentration inequalities.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "concentration inequality; isotropy",
}
@Article{ORourke:2012:NMP,
author = "Sean O'Rourke",
title = "A note on the {Marchenko--Pastur} law for a class of
random matrices with dependent entries",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "28:1--28:13",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2020",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2020",
abstract = "We consider a class of real random matrices with
dependent entries and show that the limiting empirical
spectral distribution is given by the Marchenko--Pastur
law. Additionally, we establish a rate of convergence
of the expected empirical spectral distribution.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Marchenko--Pastur law; Random Matrix Theory; Stieltjes
transform",
}
@Article{Chigansky:2012:CPA,
author = "Pavel Chigansky and Fima Klebaner",
title = "Compound {Poisson} approximation for triangular arrays
with application to threshold estimation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "29:1--29:10",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2009",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2009",
abstract = "We prove weak convergence of sums over triangular
arrays to the compound Poisson limit using Tikhomirov's
method. The result is applied to statistical estimation
of the threshold parameter in autoregressive models.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "compound Poisson; threshold estimation; Tikhomirov's
method; weak convergence",
}
@Article{Procaccia:2012:CEI,
author = "Eviatar Procaccia and Ron Rosenthal",
title = "Concentration estimates for the isoperimetric constant
of the supercritical percolation cluster",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "30:1--30:11",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2185",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2185",
abstract = "We consider the Cheeger constant $ \phi (n) $ of the
giant component of supercritical bond percolation on $
\mathbb {Z}^d / n \mathbb {Z}^d $. We show that the
variance of $ \phi (n) $ is bounded by $ \frac {\xi
}{n^d} $, where $ \xi $ is a positive constant that
depends only on the dimension $d$ and the percolation
parameter.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Isoperimetric constant; Percolation, concentration",
}
@Article{Hashorva:2012:ISD,
author = "Enkelejd Hashorva and Lanpeng Ji and Zhongquan Tan",
title = "On the infinite sums of deflated {Gaussian} products",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "31:1--31:8",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1921",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1921",
abstract = "In this paper we derive the exact tail asymptotic
behaviour of $ S_\infty = \sum_{i = 1}^\infty \lambda_i
X_i Y_i $, where $ \lambda_i, i \ge 1, $ are
non-negative square summable deflators (weights) and $
X_i, Y_i, i \ge 1, $ are independent standard Gaussian
random variables. Further, we consider the tail
asymptotics of $ S_{\infty; p} = \sum_{i = 1}^\infty
\lambda_i X_i|Y_i|^p, p > 1 $, and also discuss the
influence on the asymptotic results when $ \lambda_i
$'s are independent random variables.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "chi-square distribution; exact tail asymptotics;
Gaussian products; infinite sums; max-domain of
attraction; random deflation; regular variation",
}
@Article{Defosseux:2012:IPM,
author = "Manon Defosseux",
title = "Interacting particle models and the {Pieri}-type
formulas : the symplectic case with non equal weights",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "32:1--32:12",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2193",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2193",
abstract = "This paper studies a particle model connected to a
Pieri-type formula for the symplectic compact group.
Particles evolve independently apart from a blocking
and pushing interaction such that they remain in the
set of symplectic Gelfand-Tsetlin patterns. We show
that if only one row of the patterns is considered, one
obtains a symplectic Schur process. The model leads in
particular to the particle model with a wall defined by
Jon Warren and Peter Windridge and to a matrix model
previously studied by the author.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Gelfand-Tsetlin patterns; interacting particle model;
intertwining; random matrices; Schur processes",
}
@Article{Li:2012:SSJ,
author = "Zenghu Li and Fei Pu",
title = "Strong solutions of jump-type stochastic equations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "33:1--33:13",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1915",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1915",
abstract = "We establish the existence and uniqueness of strong
solutions to some jump-type stochastic equations under
non-Lipschitz conditions. The results improve those of
Fu and Li (2010) and Li and Mytnik (2011).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "jump-type stochastic equation; non-Lipschitz
condition; pathwise uniqueness; Strong solution",
}
@Article{Orsingher:2012:PRF,
author = "Enzo Orsingher and Mirko D'Ovidio",
title = "Probabilistic representation of fundamental solutions
to $ \frac {\partial u}{\partial t} = \kappa_m \frac
{\partial^m u}{\partial x^m} $",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "34:1--34:12",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1885",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1885",
abstract = "For the fundamental solutions of heat-type equations
of order $n$ we give a general stochastic
representation in terms of damped oscillations with
generalized gamma distributed parameters. By composing
the pseudo-process $ X_m$ related to the higher-order
heat-type equation with positively skewed stable r.v.'s
$ T^j_{1 / 3}$, $ j = 1, 2, \ldots {}, n$ we obtain
genuine r.v.'s whose explicit distribution is given for
$ n = 3$ in terms of Cauchy asymmetric laws. We also
prove that $ X_3 (T^1_{1 / 3}(\ldots {}(T^n_{(1 /
3)}(t)) \ldots {}))$ has a stable asymmetric law.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Airy functions; Cauchy distribution; fractional
diffusion equations; higher-order heat equation;
Pseudo-process; stable laws",
}
@Article{Dolgopyat:2012:SLR,
author = "Dmitry Dolgopyat and Elena Kosygina",
title = "Scaling limits of recurrent excited random walks on
integers",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "35:1--35:14",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2213",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2213",
abstract = "We describe scaling limits of recurrent excited random
walks (ERWs) on $ \mathbb {Z} $ in i.i.d. cookie
environments with a bounded number of cookies per site.
We allow both positive and negative excitations. It is
known that ERW is recurrent if and only if the expected
total drift per site, $ \delta $, belongs to the
interval $ [ - 1, 1] $. We show that if $ | \delta | <
1 $ then the diffusively scaled ERW under the averaged
measure converges to a $ (\delta, - \delta)$-perturbed
Brownian motion. In the boundary case, $ | \delta | =
1$, the space scaling has to be adjusted by an extra
logarithmic term, and the weak limit of ERW happens to
be a constant multiple of the running maximum of the
standard Brownian motion, a transient process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "branching process; cookie walk; excited random walk;
perturbed Brownian motion; random environment",
}
@Article{Nourdin:2012:CLS,
author = "Ivan Nourdin and Guillaume Poly",
title = "Convergence in law in the second {Wiener\slash Wigner}
chaos",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "36:1--36:12",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2023",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See erratum \cite{Nourdin:2012:ECL}.",
URL = "http://ecp.ejpecp.org/article/view/2023",
abstract = "Let L be the class of limiting laws associated with
sequences in the second Wiener chaos. We exhibit a
large subset $ L_0 $ of $L$ satisfying that, for any $
F_\infty $ in $ L_0$, the convergence of only a finite
number of cumulants suffices to imply the convergence
in law of any sequence in the second Wiener chaos to $
F_\infty $. This result is in the spirit of the seminal
paper by Nualart and Peccati, in which the authors
discovered the surprising fact that convergence in law
for sequences of multiple Wiener-It{\^o} integrals to
the Gaussian is equivalent to convergence of just the
fourth cumulant. Also, we offer analogues of this
result in the case of free Brownian motion and double
Wigner integrals, in the context of free
probability.\par
{\bf \url{https://doi.org/10.1214/ECP.v17-2383} An
Erratum is available in ECP volume {\bf 17} paper
number 54.}",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Convergence in law; free probability; quadratic form;
second Wiener chaos; second Wigner chaos",
}
@Article{Subramanian:2012:DCP,
author = "Sneha Subramanian",
title = "On the distribution of critical points of a
polynomial",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "37:1--37:9",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2040",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2040",
abstract = "This paper proves that if points $ Z_1, Z_2, \ldots {}
$ are chosen independently and identically using some
measure $ \mu $ from the unit circle in the complex
plane, with $ p_n(z) = (z - Z_1)(z - Z_2) \ldots {}(z -
Z_n) $, then the empirical distribution of the critical
points of $ p_n $ converges weakly to $ \mu $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "critical points; Pemantle-Rivin conjecture; random
polynomials",
}
@Article{Doney:2012:LDR,
author = "Ronald Doney and Elinor Jones",
title = "Large deviation results for random walks conditioned
to stay positive",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "38:1--38:11",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2282",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2282",
abstract = "Let $ X_1, X_2, \ldots {} $ denote independent,
identically distributed random variables with common
distribution $F$, and $S$ the corresponding random walk
with $ \rho := \lim_{n \rightarrow \infty }P(S_n > 0)$
and $ \tau := \inf \{ n \geq 1 : S_n \leq 0 \} $. We
assume that $X$ is in the domain of attraction of an $
\alpha $-stable law, and that $ P(X \in \lbrack x, x +
\Delta))$ is regularly varying at infinity, for fixed $
\Delta > 0$. Under these conditions, we find an
estimate for $ P(S_n \in \lbrack x, x + \Delta)| \tau >
n)$, which holds uniformly as $ x / c_n \rightarrow
\infty $, for a specified norming sequence $ c_n$. \par
This result is of particular interest as it is related
to the bivariate ladder height process $ ((T_n, H_n), n
\geq 0)$, where $ T_r$ is the $r$ th strict increasing
ladder time, and $ H_r = S_{T_r}$ the corresponding
ladder height. The bivariate renewal mass function $
g(n, d x) = \sum_{r = 0}^{\infty }P(T_r = n, H_r \in d
x)$ can then be written as $ g(n, d x) = P(S_n \in d x|
\tau > n)P(\tau > n)$, and since the behaviour of $
P(\tau > n)$ is known for asymptotically stable random
walks, our results can be rephrased as large deviation
estimates of $ g(n, [x, x + \Delta))$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Limit theorems; Random walks; Stable laws",
}
@Article{Balanca:2012:SIO,
author = "Paul Balan{\c{c}}a and Erick Herbin",
title = "A set-indexed {Ornstein--Uhlenbeck} process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "39:1--39:14",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1903",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1903",
abstract = "The purpose of this article is a set-indexed extension
of the well known Ornstein--Uhlenbeck process. The
first part is devoted to a stationary definition of the
random field and ends up with the proof of a complete
characterization by its $ L^2$-continuity, stationarity
and set-indexed Markov properties. This specific Markov
transition system allows to define a general
set-indexed Ornstein Uhlenbeck (SIOU) process with any
initial probability measure. Finally, in the
multiparameter case, the SIOU process is proved to
admit a natural integral representation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Markov property; multiparameter and set-indexed
processes; Ornstein--Uhlenbeck process; stationarity",
}
@Article{Tribe:2012:ODA,
author = "Roger Tribe and Jonathan Yip and Oleg Zaboronski",
title = "One dimensional annihilating and coalescing particle
systems as extended {Pfaffian} point processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "40:1--40:7",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2133",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2133",
abstract = "We prove that the multi-time particle distributions
for annihilating or coalescing Brownian motions, under
the maximal entrance law on the real line, are extended
Pfaffian point processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "annihilating Brownian motions; coalescing Brownian
motions; Extended Pfaffian point process",
}
@Article{Huss:2012:TRR,
author = "Wilfried Huss and Ecaterina Sava",
title = "Transience and recurrence of rotor-router walks on
directed covers of graphs",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "41:1--41:13",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2096",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2096",
abstract = "The aim of this note is to extend the result of Angel
and Holroyd concerning the transience and the
recurrence of transfinite rotor-router walks, for
random initial configuration of rotors on homogeneous
trees. We address the same question on directed covers
of finite graphs, which are also called trees with
finitely many cone types or periodic trees.
Furthermore, we provide an example of a directed cover
such that the rotor-router walk can be either recurrent
or transient, depending only on the planar embedding of
the periodic tree.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "directed covers; graphs; multitype branching process;
recurrence; rotor-router walks; transience",
}
@Article{Benjamini:2012:LIP,
author = "Itai Benjamini and Nicolas Curien and Agelos
Georgakopoulos",
title = "The {Liouville} and the intersection properties are
equivalent for planar graphs",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "42:1--42:5",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1913",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1913",
abstract = "It is shown that if a planar graph admits no
non-constant bounded harmonic function then the
trajectories of two independent simple random walks
intersect almost surely.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "intersection; Liouville property; Planar graphs;
Random walks",
}
@Article{Jourdain:2012:EPI,
author = "Benjamin Jourdain",
title = "Equivalence of the {Poincar{\'e}} inequality with a
transport-chi-square inequality in dimension one",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "43:1--43:12",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2115",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2115",
abstract = "In this paper, we prove that, in dimension one, the
Poincar{\'e} inequality is equivalent to a new
transport-chi-square inequality linking the square of
the quadratic Wasserstein distance with the chi-square
pseudo-distance. We also check tensorization of this
transport-chi-square inequality.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "chi-square pseudo-distance; Poincar{\'e} inequality;
transport inequality; Wasserstein distance",
}
@Article{Avena:2012:SEM,
author = "Luca Avena",
title = "Symmetric exclusion as a model of non-elliptic
dynamical random conductances",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "44:1--44:8",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2081",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2081",
abstract = "We consider a finite range symmetric exclusion process
on the integer lattice in any dimension. We interpret
it as a non-elliptic time-dependent random conductance
model by setting conductances equal to one over the
edges with end points occupied by particles of the
exclusion process and to zero elsewhere. We prove a law
of large number and a central limit theorem for the
random walk driven by such a dynamical field of
conductances using the Kipnis-Varhadan martingale
approximation. Unlike the tagged particle in the
exclusion process, which is in some sense similar to
this model, this random walk is diffusive even in the
one-dimensional nearest-neighbor symmetric case.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "exclusion process; invariance principle; law of large
numbers; Random conductances",
}
@Article{Wojtylak:2012:CSR,
author = "Micha{\l} Wojtylak",
title = "On a class of {$H$}-selfadjont random matrices with
one eigenvalue of nonpositive type",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "45:1--45:14",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2148",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2148",
abstract = "Large $H$-selfadjoint random matrices are considered.
The matrix $H$ is assumed to have one negative
eigenvalue, hence the matrix in question has precisely
one eigenvalue of nonpositive type. It is showed that
this eigenvalue converges in probability to a
deterministic limit. The weak limit of distribution of
the real eigenvalues is investigated as well.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "$\Pi_1$-space; eigenvalue; limit distribution of
eigenvalues; Random matrix; Wigner matrix",
}
@Article{Ano:2012:PUM,
author = "Katsunori Ano and Roman Ivanov",
title = "On predicting the ultimate maximum for exponential
{L{\'e}vy} processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "46:1--46:9",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1805",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1805",
abstract = "We consider a problem of predicting of the ultimate
maximum of the process over a finite interval of time.
Mathematically, this problem relates to a particular
optimal stopping problem. In this paper we discuss
exponential L{\'e}vy processes. As the L{\'e}vy
processes, we discuss $ \alpha $-stable L{\'e}vy
processes, $ 0 < \alpha \leq 2$, and generalized
hyperbolic L{\'e}vy processes. The method of solution
uses the representations of these processes as
time-changed Brownian motions with drift. Our results
generalize results of papers by Toit and Peskir and by
Shiryaev and Xu, and Zhou.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "exponential L{\'e}vy process; optimal stopping;
predicting; selling of asset; utility function",
}
@Article{Frikha:2012:CBS,
author = "Noufel Frikha and St{\'e}phane Menozzi",
title = "Concentration bounds for stochastic approximations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "47:1--47:15",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1952",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1952",
abstract = "We obtain non asymptotic concentration bounds for two
kinds of stochastic approximations. We first consider
the deviations between the expectation of a given
function of an Euler like discretization scheme of some
diffusion process at a fixed deterministic time and its
empirical mean obtained by the Monte Carlo procedure.
We then give some estimates concerning the deviation
between the value at a given time-step of a stochastic
approximation algorithm and its target. Under suitable
assumptions both concentration bounds turn out to be
Gaussian. The key tool consists in exploiting
accurately the concentration properties of the
increments of the schemes. Also, no specific
non-degeneracy conditions are assumed.
{\bf An Erratum is available in
\url{https://doi.org/10.1214/ECP.v17-2495} ECP volume
17 paper number 60.}",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Non asymptotic bounds, Euler scheme, Stochastic
approximation algorithms, Gaussian concentration",
}
@Article{Perkowski:2012:CM,
author = "Nicolas Perkowski and Johannes Ruf",
title = "Conditioned martingales",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "48:1--48:12",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1955",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1955",
abstract = "It is well known that upward conditioned Brownian
motion is a three-dimensional Bessel process, and that
a downward conditioned Bessel process is a Brownian
motion. We give a simple proof for this result, which
generalizes to any continuous local martingale and
clarifies the role of finite versus infinite time in
this setting. As a consequence, we can describe the law
of regular diffusions that are conditioned upward or
downward.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bessel process; change of measure; diffusion; Doob's
h-transform; downward conditioning; local martingale;
nullset; upward conditioning",
}
@Article{Fittipaldi:2012:SAC,
author = "Maria Fittipaldi and Joaquin {Fontbona T.}",
title = "On {SDE} associated with continuous-state branching
processes conditioned to never be extinct",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "49:1--49:13",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1972",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1972",
abstract = "We study the pathwise description of a (sub-)critical
continuous-state branching process (CSBP) conditioned
to be never extinct, as the solution to a stochastic
differential equation driven by Brownian motion and
Poisson point measures. The interest of our approach,
which relies on applying Girsanov theorem on the SDE
that describes the unconditioned CSBP, is that it
points out an explicit mechanism to build the
immigration term appearing in the conditioned process,
by randomly selecting jumps of the original one. These
techniques should also be useful to represent more
general $h$-transforms of diffusion-jump processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Continuous-state branching processes; Immigration;
Non-extinction; Stochastic Differential Equations",
}
@Article{Klimmek:2012:WPC,
author = "Martin Klimmek",
title = "The {Wronskian} parametrises the class of diffusions
with a given distribution at a random time",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "50:1--50:8",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1976",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1976",
abstract = "We provide a complete characterisation of the class of
one-dimensional time-homogeneous diffusions consistent
with a given law at an exponentially distributed time
using classical results in diffusion theory. To
illustrate we characterise the class of diffusions with
the same distribution as Brownian motion at an
exponentially distributed time.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Diffusion; exponential time; h-transform; inverse
problem; local-martingale",
}
@Article{Boucheron:2012:CIO,
author = "St{\'e}phane Boucheron and Maud Thomas",
title = "Concentration inequalities for order statistics",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "51:1--51:12",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2210",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2210",
abstract = "This note describes non-asymptotic variance and tail
bounds for order statistics of samples of independent
identically distributed random variables. When the
sampling distribution belongs to a maximum domain of
attraction, these bounds are checked to be
asymptotically tight. When the sampling distribution
has a non decreasing hazard rate, we derive an
exponential Efron-Stein inequality for order
statistics, that is an inequality connecting the
logarithmic moment generating function of order
statistics with exponential moments of Efron-Stein
(jackknife) estimates of variance. This connection is
used to derive variance and tail bounds for order
statistics of Gaussian samples that are not within the
scope of the Gaussian concentration inequality. Proofs
are elementary and combine R{\'e}nyi's representation
of order statistics with the entropy approach to
concentration of measure popularized by M. Ledoux.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "concentration inequalities; entropy method; order
statistics",
}
@Article{Hsu:2012:TIQ,
author = "Daniel Hsu and Sham Kakade and Tong Zhang",
title = "A tail inequality for quadratic forms of {subGaussian}
random vectors",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "52:1--52:6",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2079",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2079",
abstract = "This article proves an exponential probability tail
inequality for positive semidefinite quadratic forms in
a subGaussian random vector. The bound is analogous to
one that holds when the vector has independent Gaussian
entries.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "quadratic form; subGaussian chaos; subGaussian random
vectors; Tail inequality",
}
@Article{Watbled:2012:SAF,
author = "Fr{\'e}d{\'e}rique Watbled",
title = "Sharp asymptotics for the free energy of 1+1
dimensional directed polymers in an infinitely
divisible environment",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "53:1--53:9",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2221",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2221",
abstract = "We give sharp estimate for the free energy of directed
polymers in random environment in dimension 1+1. This
estimate was known for a Gaussian environment, we
extend it to the case where the law of the environment
is infinitely divisible.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "directed polymers in random environment; FKG
inequality; free energy; infinite divisibility",
}
@Article{Nourdin:2012:ECL,
author = "Ivan Nourdin and Guillaume Poly",
title = "Erratum: {Convergence in law in the second
Wiener\slash Wigner chaos}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "54:1--54:3",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2383",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See \cite{Nourdin:2012:CLS}.",
URL = "http://ecp.ejpecp.org/article/view/2383",
abstract = "This is an erratum for paper ``Convergence in law in
the second Wiener\slash Wigner chaos'', which appeared
in \url{https://doi.org/10.1214/ECP.v17-2023} ECP
volume {\bf 17} paper number 36.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "second Wiener chaos; second Wigner chaos",
}
@Article{Madan:2012:MWI,
author = "Dilip Madan and Marc Yor",
title = "Moments of {Wiener} integrals for subordinators",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "55:1--55:8",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2206",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2206",
abstract = "Moments formulae for Wiener integrals of a
subordinator with exponential moments are obtained in
terms of the general Bell polynomials and the moments
of the L{\'e}vy measure of this subordinator. We also
express the Appell and Scheffer polynomials associated
to a random variable in terms of the Bell
polynomials.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Appell, Bell and Scheffer polynomials; L{\'e}vy
measure; Subordinator",
}
@Article{Benaim:2012:QES,
author = "Michel Bena{\"\i}m and St{\'e}phane {Le Borgne} and
Florent Malrieu and Pierre-Andr{\'e} Zitt",
title = "Quantitative ergodicity for some switched dynamical
systems",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "56:1--56:14",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1932",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1932",
abstract = "We provide quantitative bounds for the long time
behavior of a class of Piecewise Deterministic Markov
Processes with state space $ \mathbb {R}^d \times E $
where $E$ is a finite set. The continuous component
evolves according to a smooth vector field that it
switched at the jump times of the discrete coordinate.
The jump rates may depend on the whole position of the
process. Under regularity assumptions on the jump rates
and stability conditions for the vector fields we
provide explicit exponential upper bounds for the
convergence to equilibrium in terms of Wasserstein
distances.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Coupling; Ergodicity; Linear Differential Equations;
Piecewise Deterministic Markov Process; Switched
dynamical systems; Wasserstein distance",
}
@Article{Nachmias:2012:NAC,
author = "Asaf Nachmias and Yuval Peres",
title = "Non-amenable {Cayley} graphs of high girth have $ p_c
< p_u $ and mean-field exponents",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "57:1--57:8",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2139",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2139",
abstract = "In this note we show that percolation on non-amenable
Cayley graphs of high girth has a phase of
non-uniqueness, i.e., $ p_c < p_u $. Furthermore, we
show that percolation and self-avoiding walk on such
graphs have mean-field critical exponents. In
particular, the self-avoiding walk has positive
speed.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Non-amenable graphs; Percolation; Self avoiding walk",
}
@Article{vandenBerg:2012:SLC,
author = "Jacob van den Berg and Rene Conijn",
title = "On the size of the largest cluster in 2D critical
percolation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "58:1--58:13",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2263",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2263",
abstract = "We consider (near-)critical percolation on the square
lattice. Let $ \mathcal {M}_n $ be the size of the
largest open cluster contained in the box $ [ - n, n]^2
$, and let $ \pi (n) $ be the probability that there is
an open path from $O$ to the boundary of the box. It is
well-known that for all $ 0 < a < b$ the probability
that $ \mathcal {M}_n$ is smaller than $ a n^2 \pi (n)$
and the probability that $ \mathcal {M}_n$ is larger
than $ b n^2 \pi (n)$ are bounded away from $0$ as $ n
\rightarrow \infty $. It is a natural question, which
arises for instance in the study of so-called
frozen-percolation processes, if a similar result holds
for the probability that $ \mathcal {M}_n$ is {\em
between} $ a n^2 \pi (n)$ and $ b n^2 \pi (n)$. By a
suitable partition of the box, and a careful
construction involving the building blocks, we show
that the answer to this question is affirmative. The
`sublinearity' of $ 1 / \pi (n)$ appears to be
essential for the argument.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Cluster size; Critical percolation",
}
@Article{Fan:2012:LDE,
author = "Xiequan Fan and Ion Grama and Quansheng Liu",
title = "Large deviation exponential inequalities for
supermartingales",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "59:1--59:8",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2318",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2318",
abstract = "Let $ (X_i, \mathcal {F}_i)_{i \geq 1} $ be a sequence
of supermartingale differences and let $ S_k = \sum_{i
= 1}^k X_i $. We give an exponential moment condition
under which $ \mathbb {P}(\max_{1 \leq k \leq n} S_k
\geq n) = O(\exp \{ - C_1 n^{\alpha } \}), $ $ n
\rightarrow \infty, $ where $ \alpha \in (0, 1) $ is
given and $ C_1 > 0 $ is a constant. We also show that
the power $ \alpha $ is optimal under the given moment
condition.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bernstein type inequality; exponential inequality;
Large deviation; martingales",
}
@Article{Frikha:2012:ECB,
author = "Noufel Frikha and St{\'e}phane Menozzi",
title = "Erratum: Concentration bounds for stochastic
approximation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "60:1--60:2",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2495",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2495",
abstract = "This is an erratum for paper ``Concentration bounds
for stochastic approximation'', which appeared in
\url{https://doi.org/10.1214/ECP.v17-1952} ECP volume
{\bf 17} paper number 47.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Euler scheme; Gaussian concentration; Non asymptotic
bounds; stochastic approximation algorithms",
}
@Article{Mijatovic:2012:CIF,
author = "Aleksandar Mijatovic and Mikhail Urusov",
title = "Convergence of integral functionals of one-dimensional
diffusions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "61:1--61:13",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-1825",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1825",
abstract = "In this paper we describe the pathwise behaviour of
the integral functional $ \int_0^t f(Y_u) \, d u $ for
any $ t \in [0, \zeta] $, where $ \zeta $ is (a
possibly infinite) exit time of a one-dimensional
diffusion process $Y$ from its state space, $f$ is a
nonnegative Borel measurable function and the
coefficients of the SDE solved by $Y$ are only required
to satisfy weak local integrability conditions. Two
proofs of the deterministic characterisation of the
convergence of such functionals are given: the problem
is reduced in two different ways to certain path
properties of Brownian motion where either the Williams
theorem and the theory of Bessel processes or the first
Ray-Knight theorem can be applied to prove the
characterisation. As a simple application of the main
results we give a short proof of Feller's test for
explosion.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bessel process; Integral functional; local time;
one-dimensional diffusion; Ray-Knight theorem; Williams
theorem",
}
@Article{Cetin:2012:FAM,
author = "Umut {\c{C}}etin",
title = "Filtered {Az{\'e}ma} martingales",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "62:1--62:13",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2310",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2310",
abstract = "We study the optional projection of a standard
Brownian motion on the natural filtration of certain
kinds of observation processes. The observation
process, $Y$, is defined as a solution of a stochastic
differential equation such that it reveals some
(possibly noisy) information about the signs of the
Brownian motion when $Y$ hits $0$. As such, the
associated optional projections are related to
Az{\'e}ma's martingales which are obtained by
projecting the Brownian motion onto the filtration
generated by observing its signs.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Az{\'e}ma's martingale; excursions of Brownian motion;
local times; optional projection; skew Brownian
motion",
}
@Article{Vakeroudis:2012:SPW,
author = "Stavros Vakeroudis and Marc Yor",
title = "A scaling proof for {Walsh}'s {Brownian} motion
extended arc-sine law",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "17",
pages = "63:1--63:9",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v17-2319",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2319",
abstract = "We present a new proof of the extended arc-sine law
related to Walsh's Brownian motion, known also as
Brownian spider. The main argument mimics the scaling
property used previously, in particular by D. Williams,
in the 1- dimensional Brownian case, which can be
generalized to the multivariate case. A discussion
concerning the time spent positive by a skew Bessel
process is also presented.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Arc-sine law, Brownian spider, Skew Bessel process,
Stable variables, Subordinators, Walsh Brownian
motion.",
}
@Article{Buckley:2013:AHK,
author = "Stephen Buckley",
title = "Anomalous heat kernel behaviour for the dynamic random
conductance model",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "1:1--1:11",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2525",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2525",
abstract = "We introduce the time dynamic random conductance model
and consider the heat kernel for the random walk on
this environment. In the case where conductances are
bounded above, an example environment is presented
which exhibits heat kernel decay that is asymptotically
slower than in the well studied time homogeneous case -
being close to $ O \left (n^{-1} \right) $ as opposed
to $ O \left (n^{-2} \right) $. The example environment
given is a modification of an environment introduced in
Berger, Biskup, Hoffman and Kozma (2008).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "heat kernel; random conductances; random walk in
random environment",
}
@Article{Chen:2013:NFP,
author = "Yu-Ting Chen and Yuan-Chung Sheu and Ming-Chi Chang",
title = "A note on first passage functionals for
hyper-exponential jump-diffusion processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "2:1--2:8",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2017",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2017",
abstract = "This investigation concerns the hyper-exponential
jump-diffusion processes. Following the exposition of
the two-sided exit problem by Kyprianou, A. E., and
Asmussen, S. and Albrecher, H., this study investigates
first passage functionals for these processes. The
corresponding boundary value problems are solved to
obtain an explicit formula for the first passage
functionals.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "first passage functional; Hyper-exponential
jump-diffusion process; two-sided exit problem",
}
@Article{Berend:2013:CMM,
author = "Daniel Berend and Aryeh Kontorovich",
title = "On the concentration of the missing mass",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "3:1--3:7",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2359",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2359",
abstract = "A random variable is sampled from a discrete
distribution. The missing mass is the probability of
the set of points not observed in the sample. We
sharpen and simplify McAllester and Ortiz's results
(JMLR, 2003) bounding the probability of large
deviations of the missing mass. Along the way, we
refine and rigorously prove a fundamental inequality of
Kearns and Saul (UAI, 1998).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "missing mass, Hoeffding inequality, measure
concentration",
}
@Article{Katori:2013:CBM,
author = "Makoto Katori and Hideki Tanemura",
title = "Complex {Brownian} motion representation of the
{Dyson} model",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "4:1--4:16",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2554",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2554",
abstract = "Dyson's Brownian motion model with the parameter $
\beta = 2 $, which we simply call the Dyson model in
the present paper, is realized as an $h$-transform of
the absorbing Brownian motion in a Weyl chamber of type
A. Depending on initial configuration with a finite
number of particles, we define a set of entire
functions and introduce a martingale for a system of
independent complex Brownian motions (CBMs), which is
expressed by a determinant of a matrix with elements
given by the conformal transformations of CBMs by the
entire functions. We prove that the Dyson model can be
represented by the system of independent CBMs weighted
by this determinantal martingale. From this CBM
representation, the Eynard-Mehta-type correlation
kernel is derived and the Dyson model is shown to be
determinantal. The CBM representation is a useful
extension of $h$-transform, since it works also in
infinite particle systems. Using this representation,
we prove the tightness of a series of processes, which
converges to the Dyson model with an infinite number of
particles, and the noncolliding property of the limit
process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "complex Brownian motions; conformal martingales;
determinantal process; Dyson model; entire functions;
h-transform; noncolliding property; tightness",
}
@Article{Maillard:2013:NSP,
author = "Pascal Maillard",
title = "A note on stable point processes occurring in
branching {Brownian} motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "5:1--5:9",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2390",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2390",
abstract = "We call a point process $Z$ on $ \mathbb R$ {\em
exp-1-stable\/} if for every $ \alpha, \beta \in
\mathbb R$ with $ e^\alpha + e^\beta = 1$, $Z$ is equal
in law to $ T_\alpha Z + T_\beta Z'$, where $ Z'$ is an
independent copy of $Z$ and $ T_x$ is the translation
by $x$. Such processes appear in the study of the
extremal particles of branching Brownian motion and
branching random walk and several authors have proven
in that setting the existence of a point process $D$ on
$ \mathbb R$ such that $Z$ is equal in law to $ \sum_{i
= 1}^\infty T_{\xi_i} D_i$, where $ (\xi_i)_{i \ge 1}$
are the atoms of a Poisson process of intensity $
e^{-x} \, \mathrm d x$ on $ \mathbb R$ and $ (D_i)_{i
\ge 1}$ are independent copies of $D$ and independent
of $ (\xi_i)_{i \ge 1}$. In this note, we show how this
decomposition follows from the classic {\em LePage
decomposition\/} of a (union)-stable point process.
Moreover, we give a short proof of it in the general
case of random measures on $ \mathbb R$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "branching Brownian motion; branching random walk;
point process; random measure; stable distribution",
}
@Article{Dominguez-Molina:2013:CRH,
author = "J. Armando Dominguez-Molina and V{\'\i}ctor
P{\'e}rez-Abreu and Alfonso Rocha-Arteaga",
title = "Covariation representations for {Hermitian L{\'e}vy}
process ensembles of free infinitely divisible
distributions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "6:1--6:14",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2113",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2113",
abstract = "It is known that the so-called Bercovici-Pata
bijection can be explained in terms of certain
Hermitian random matrix ensembles $ (M_d)_{d \geq 1} $
whose asymptotic spectral distributions are free
infinitely divisible. We investigate Hermitian L{\'e}vy
processes with jumps of rank one associated to these
random matrix ensembles introduced by Benaych--Georges
and Cabanal--Duvillard. A sample path approximation by
covariation processes for these matrix L{\'e}vy
processes is obtained. As a general result we prove
that any $ d \times d $ complex matrix subordinator
with jumps of rank one is the quadratic variation of a
$ \mathbb {C}^d$-valued L{\'e}vy process. In
particular, we have the corresponding result for matrix
subordinators with jumps of rank one associated to the
random matrix ensembles $ (M_d)_{d \geq 1}$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Infinitely divisible random matrix, matrix
subordinator, Bercovici-Pata bijection, matrix
semimartingale, matrix compound Poisson.",
}
@Article{Ley:2013:SDA,
author = "Christophe Ley and Yvik Swan",
title = "{Stein}'s density approach and information
inequalities",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "7:1--7:14",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2578",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2578",
abstract = "We provide a new perspective on Stein's so-called
density approach by introducing a new operator and
characterizing class which are valid for a much wider
family of probability distributions on the real line.
We prove an elementary factorization property of this
operator and propose a new Stein identity which we use
to derive information inequalities in terms of what we
call the {"generalized} Fisher information {distance"}.
We provide explicit bounds on the constants appearing
in these inequalities for several important cases. We
conclude with a comparison between our results and
known results in the Gaussian case, hereby improving on
several known inequalities from the literature.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "generalized Fisher information; magic factors;
Pinsker's inequality; probability metrics; Stein's
density approach",
}
@Article{Bianchi:2013:UIS,
author = "Luigi Bianchi",
title = "Uniqueness for an inviscid stochastic dyadic model on
a tree",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "8:1--8:12",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2382",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2382",
abstract = "In this paper we prove that the lack of uniqueness for
solutions of the tree dyadic model of turbulence is
overcome with the introduction of a suitable noise. The
uniqueness is a weak probabilistic uniqueness for all $
l^2$-initial conditions and is proven using a technique
relying on the properties of the $q$-matrix associated
to a continuous time Markov chain.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "dyadic model; fluid dynamics; Girsanov's transform;
multiplicative noise; q-matrix; shell models; SPDE;
tree dyadic model",
}
@Article{Garet:2013:CBR,
author = "Olivier Garet and R{\'e}gine Marchand",
title = "The critical branching random walk in a random
environment dies out",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "9:1--9:15",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2438",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2438",
abstract = "We study the possibility for branching random walks in
random environment (BRWRE) to survive. The particles
perform simple symmetric random walks on the
$d$-dimensional integer lattice, while at each time
unit, they split into independent copies according to
time-space i.i.d. offspring distributions. As noted by
Comets and Yoshida, the BRWRE is naturally associated
with the directed polymers in random environment
(DPRE), for which the quantity $ \Psi $ called the free
energy is well studied. Comets and Yoshida proved that
there is no survival when $ \Psi < 0$ and that survival
is possible when $ \Psi > 0$. We proved here that,
except for degenerate cases, the BRWRE always die when
$ \Psi = 0$. This solves a conjecture of Comets and
Yoshida.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "block construction; branching random walk; critical
behavior; random environment; renormalization;
survival",
}
@Article{Michna:2013:EFS,
author = "Zbigniew Michna",
title = "Explicit formula for the supremum distribution of a
spectrally negative stable process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "10:1--10:6",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2236",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2236",
abstract = "In this article we get simple formulas for $ E \sup_{s
\leq t}X(s) $ where $X$ is a spectrally positive or
negative L{\'e}vy process with infinite variation. As a
consequence we derive a generalization of the
well-known formula for the supremum distribution of
Wiener process that is we obtain $ P(\sup_{s \leq
t}Z_{\alpha }(s) \geq u) = \alpha \, P(Z_{\alpha }(t)
\geq u)$ for $ u \geq 0$ where $ Z_{\alpha }$ is a
spectrally negative $ \alpha $-stable L{\'e}vy process
with $ 1 < \alpha \leq 2$ which also stems from
Kendall's identity for the first crossing time. Our
proof uses a formula for the supremum distribution of a
spectrally positive L{\'e}vy process which follows
easily from the elementary Seal's formula.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "L{\'e}vy process, distribution of the supremum of a
stochastic process, $\alpha$-stable L{\'e}vy process",
}
@Article{Bierme:2013:FPF,
author = "Hermine Bierm{\'e} and Yann Demichel and Anne
Estrade",
title = "Fractional {Poisson} field and fractional {Brownian}
field: why are they resembling but different?",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "11:1--11:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-1939",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1939",
abstract = "The fractional Poisson field (fPf) is constructed by
considering the number of balls falling down on each
point of $ \mathbb R^D $, when the centers and the
radii of the balls are thrown at random following a
Poisson point process in $ \mathbb R^D \times \mathbb
R^+ $ with an appropriate intensity measure. It
provides a simple description for a non Gaussian random
field that is centered, has stationary increments and
has the same covariance function as the fractional
Brownian field (fBf). The present paper is concerned
with specific properties of the fPf, comparing them to
their analogues for the fBf. On the one hand, we
concentrate on the finite-dimensional distributions
which reveal strong differences between the Gaussian
world of the fBf and the Poissonian world of the fPf.
We provide two different representations for the
marginal distributions of the fPf: as a Chentsov field,
and on a regular grid in $ \mathbb R^D $ with a
numerical procedure for simulations. On the other hand,
we prove that the Hurst index estimator based on
quadratic variations which is commonly used for the fBf
is still strongly consistent for the fPf. However the
computations for the proof are very different from the
usual ones.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Chentsov field; Fractional Brownian field; Fractional
process; Hurst index; Poisson point process; Poisson
random measure; Random field",
}
@Article{Meiners:2013:ANA,
author = "Raphael Meiners and Anselm Reichenbachs",
title = "On the accuracy of the normal approximation for the
free energy in the Random Energy Model",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "12:1--12:11",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2377",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2377",
abstract = "In the present paper we consider the fluctuations of
the free energy in the random energy model (REM) on a
moderate deviation scale. We find that for high
temperatures the normal approximation holds only in a
narrow range of scalings away from the CLT. For
scalings of higher order, probabilities of moderate
deviations decay faster than exponentially.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "free energy; large deviations; moderate deviations;
Random Energy Model",
}
@Article{Toth:2013:CTM,
author = "B{\'a}lint T{\'o}th",
title = "Comment on a theorem of {M. Maxwell} and {M.
Woodroofe}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "13:1--13:4",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2366",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2366",
abstract = "We present a direct derivation of the theorem of M.
Maxwell and M. Woodroofe (Ann. Probab. vol. 28 (2000)
713-724), on martingale approximation of additive
functionals of stationary Markov processes, from the
non-reversible version of the Kipnis-Varadhan
theorem.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "CLT, Markov process, martingale approximation",
}
@Article{Jansen:2013:GRC,
author = "Sabine Jansen and Noemi Kurt",
title = "Graphical representation of certain moment dualities
and application to population models with balancing
selection",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "14:1--14:15",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2194",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2194",
abstract = "We investigate dual mechanisms for interacting
particle systems. Generalizing an approach of Alkemper
and Hutzenthaler in the case of coalescing duals, we
show that a simple linear transformation leads to a
moment duality of suitably rescaled processes. More
precisely, we show how dualities of interacting
particle systems of the form $ H(A, B) = q^{|A \cap
B|}, A, B \subset \{ 0, 1 \}^N, q \in [ - 1, 1), $ are
rescaled to yield moment dualities of rescaled
processes. We discuss in particular the case $ q = - 1,
$ which explains why certain population models with
balancing selection have an annihilating dual process.
We also consider different values of $ q, $ and answer
a question by Alkemper and Hutzenthaler.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Markov processes, duality, interacting particle
systems, graphical representation, annihilation,
selection",
}
@Article{Janson:2013:MLM,
author = "Svante Janson",
title = "Moments of the location of the maximum of {Brownian}
motion with parabolic drift",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "15:1--15:8",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2330",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2330",
abstract = "We derive integral formulas, involving the Airy
function, for moments of the time a two-sided Brownian
motion with parabolic drift attains its maximum.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "brownian motion; Chernoff's distribution; parabolic
drift",
}
@Article{Tkocz:2013:NTP,
author = "Tomasz Tkocz",
title = "A note on the tensor product of two random unitary
matrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "16:1--16:7",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2484",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2484",
abstract = "In this note we consider the point process of
eigenvalues of the tensor product of two independent
random unitary matrices of size m by m and n by n. When
n becomes large, the process behaves like the
superposition of m independent sine processes. When m
and n go to infinity, we obtain the Poisson point
process in the limit.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Circular Unitary Ensemble; Poisson point process;
Random matrices; Sine point process; Tensor product",
}
@Article{Loehr:2013:EGP,
author = "Wolfgang Loehr",
title = "Equivalence of {Gromov--Prohorov}- and {Gromov}'s {$
\underline \Box_\lambda $}-metric on the space of
metric measure spaces",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "17:1--17:10",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2268",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2268",
abstract = "The space of metric measure spaces (complete separable
metric spaces with a probability measure) is becoming
more and more important as state space for stochastic
processes. Of particular interest is the subspace of
(continuum) metric measure trees. Greven, Pfaffelhuber
and Winter introduced the Gromov--Prohorov metric $
d_{\mathrm {GP}} $ on the space of metric measure
spaces and showed that it induces the Gromov-weak
topology. They also conjectured that this topology
coincides with the topology induced by Gromov's $
\underline \Box_1 $ metric. Here, we show that this is
indeed true, and the metrics are even bi-Lipschitz
equivalent. More precisely, $ d_{\mathrm {GP}} = \frac
12 \underline \Box_{\frac 12} $, and hence $ d_{\mathrm
{GP}} \le \underline \Box_1 \le 2 d_{\mathrm {GP}} $.
The fact that different approaches lead to equivalent
metrics underlines their importance and also that of
the induced Gromov-weak topology. As an application, we
give an easy proof of the known fact that the map
associating to a lower semi-continuous excursion the
coded $ \mathbb {R}$-tree is Lipschitz continuous when
the excursions are endowed with the (non-separable)
uniform metric. We also introduce a new, weaker, metric
topology on excursions, which has the advantage of
being separable and making the space of bounded
excursions a Lusin space. We obtain continuity also for
this new topology.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "space of metric measure spaces, Gromov--Prohorov
metric, Gromov's box-metric, Gromov-weak topology, real
tree, coding trees by excursions, Lusin topology on
excursions",
}
@Article{ODonnell:2013:SKS,
author = "Ryan O'Donnell and Karl Wimmer",
title = "Sharpness of {KKL} on {Schreier} graphs",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "18:1--18:12",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-1961",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1961",
abstract = "Recently, the Kahn-Kalai-Linial (KKL) Theorem on
influences of functions on $ \{ 0, 1 \}^n $ was
extended to the setting of functions on Schreier
graphs. Specifically, it was shown that for an
undirected Schreier graph $ \text {Sch}(G, X, U) $ with
log Sobolev constant $ \rho $ and generating set $U$
closed under conjugation, if $ f : X \to \{ 0, 1 \} $
then\par
$$ \mathcal {E}[f] \gtrsim \log (1 / \text
{MaxInf}[f]) \cdot \rho \cdot {\bf Var}[f]. $$
Here $ \mathcal {E}[f]$ denotes the average of $f$'s
influences, and $ \text {MaxInf}[f]$ denotes their
maximum. In this work we investigate the extent to
which this result is sharp. We show:\par
1. The condition that $U$ is closed under conjugation
cannot in general be eliminated.\par
2. The log-Sobolev constant cannot be replaced by the
modified log-Sobolev constant.\par
3. The result cannot be improved for the Cayley graph
on $ S_n$ with transpositions.\par
4. The result {\em can\/} be improved for the Cayley
graph on $ \mathbb {Z}_m^n$ with standard
generators.\par
5. Talagrand's strengthened version of KKL also holds
in the Schreier graph setting:\par
$$ \mathrm {avg}_{u \in U} \{ \mathrm {Inf}_u[f] /
\log (1 / \mathrm {Inf}_u[f]) \} \gtrsim \rho \cdot
{\bf Var}[f]. $$",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "boolean functions; Cayley graphs; KKL; log-sobolev
constant; Orlicz norms; Schreier graphs",
}
@Article{Stenlund:2013:LLT,
author = "Mikko Stenlund",
title = "A local limit theorem for random walks in balanced
environments",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "19:1--19:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2336",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2336",
abstract = "Central limit theorems for random walks in quenched
random environments have attracted plenty of attention
in the past years. More recently still, finer local
limit theorems - yielding a Gaussian density multiplied
by a highly oscillatory modulating factor - for such
models have been obtained. In the one-dimensional
nearest-neighbor case with i.i.d. transition
probabilities, local limits of uniformly elliptic
ballistic walks are now well understood. We complete
the picture by proving a similar result for the only
recurrent case, namely the balanced one, in which such
a walk is diffusive. The method of proof is, out of
necessity, entirely different from the ballistic
case.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Balanced random environment, local limit theorem, Nash
inequality",
}
@Article{Ondrejat:2013:EPM,
author = "Martin Ondrejat and Jan Seidler",
title = "On existence of progressively measurable
modifications",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "20:1--20:6",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2548",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2548",
abstract = "In this note we provide a short and simple proof that
every adapted measurable stochastic process admits a
progressively measurable modification.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "modification; progressive measurability",
}
@Article{Liu:2013:ASS,
author = "Hanbing Liu and Juan Yang",
title = "An approximation scheme of stochastic {Stokes}
equations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "21:1--21:10",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2374",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2374",
abstract = "This work is concerned with the approximation to the
solutions of the stochastic Stokes equations by the
splitting up method. We apply the resolvent operator to
evaluate the solution of the deterministic equations at
the endpoints of every small interval, and the error is
estimated.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Ejsmont:2013:NCF,
author = "Wiktor Ejsmont",
title = "Noncommutative characterization of free {Meixner}
processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "22:1--22:12",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2356",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2356",
abstract = "In this article we give a purely noncommutative
criterion for the characterization of free Meixner
random variables. We prove that some families of free
Meixner distributions can be described in terms of the
conditional expectation, which has no classical
analogue. We also show a generalization of Speicher's
formula (relating moments and free cumulants) and
establish a new relation in free probability.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "conditional expectation; free cumulants; free Meixner
law; Laha--Lukacs theorem; noncommutative regression",
}
@Article{Devillers:2013:MVR,
author = "Olivier Devillers and Marc Glisse and Xavier Goaoc and
Guillaume Moroz and Matthias Reitzner",
title = "The monotonicity of $f$-vectors of random polytopes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "23:1--23:8",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2469",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2469",
abstract = "Let $K$ be a compact convex body in $ {\mathbb R}^d$,
let $ K_n$ be the convex hull of $n$ points chosen
uniformly and independently in $K$, and let $ f_i(K_n)$
denote the number of $i$-dimensional faces of $ K_n$.
We show that for planar convex sets, $ E[f_0 (K_n)]$ is
increasing in $n$. In dimension $ d \geq 3$ we prove
that if $ \lim_{n \to \infty } \frac {E[f_{d -
1}(K_n)]}{An^c} = 1$ for some constants $A$ and $ c >
0$ then the function $ n \mapsto E[f_{d - 1}(K_n)]$ is
increasing for $n$ large enough. In particular, the
number of facets of the convex hull of $n$ random
points distributed uniformly and independently in a
smooth compact convex body is asymptotically
increasing. Our proof relies on a {\em random
sampling\/} argument.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Complexity; Computational geometry; Convex hull",
}
@Article{Tappe:2013:YWT,
author = "Stefan Tappe",
title = "The {Yamada--Watanabe} theorem for mild solutions to
stochastic partial differential equations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "24:1--24:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2392",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2392",
abstract = "We prove the Yamada--Watanabe theorem for semilinear
stochastic partial differential equations with
path-dependent coefficients. The so-called {"method} of
the moving {frame"} allows us to reduce the proof to
the Yamada--Watanabe theorem for stochastic
differential equations in infinite dimensions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "martingale solution; mild solution; pathwise
uniqueness; Stochastic partial differential equation",
}
@Article{Bordenave:2013:ERM,
author = "Charles Bordenave",
title = "On {Euclidean} random matrices in high dimension",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "25:1--25:8",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2340",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2340",
abstract = "In this note, we study the n x n random Euclidean
matrix whose entry (i, j) is equal to f (|| Xi - Xj ||)
for some function f and the Xi's are i.i.d. isotropic
vectors in Rp. In the regime where n and p both grow to
infinity and are proportional, we give some sufficient
conditions for the empirical distribution of the
eigenvalues to converge weakly. We illustrate our
result on log-concave random vectors.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Euclidean random matrices, Marcenko-Pastur
distribution, Log-concave distribution.",
}
@Article{Fradon:2013:SDE,
author = "Myriam Fradon",
title = "Stochastic differential equations on domains defined
by multiple constraints",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "26:1--26:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2730",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2730",
abstract = "We present simple assumptions on the constraints
defining a hard core dynamics for the associated
reflected stochastic differential equation to have a
unique strong solution. Time-reversibility is proven
for gradient systems with normal or co-normal
reflection. An illustration is given concerning the
clustering at equilibrium of particles around a large
attractive sphere.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "geometrical constraints; hard core interaction; local
time; Skorokhod Equation",
}
@Article{Nechita:2013:RPQ,
author = "Ion Nechita and Cl{\'e}ment Pellegrini",
title = "Random pure quantum states via unitary {Brownian}
motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "27:1--27:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2426",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2426",
abstract = "We introduce a new family of probability distributions
on the set of pure states of a finite dimensional
quantum system. Without any a priori assumptions, the
most natural measure on the set of pure state is the
uniform (or Haar) measure. Our family of measures is
indexed by a time parameter $t$ and interpolates
between a deterministic measure ($ t = 0$) and the
uniform measure ($ t = \infty $). The measures are
constructed using a Brownian motion on the unitary
group $ \mathcal U_N$. Remarkably, these measures have
a $ \mathcal U_{N - 1}$ invariance, whereas the usual
uniform measure has a $ \mathcal U_N$ invariance. We
compute several averages with respect to these measures
using as a tool the Laplace transform of the
coordinates.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "quantum states, unitary Brownian motion",
}
@Article{Benjamini:2013:ARR,
author = "Itai Benjamini and Hilary Finucane and Romain
Tessera",
title = "Algebraically recurrent random walks on groups",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "28:1--28:8",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2519",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2519",
abstract = "Initial steps are presented towards understanding
which finitely generated groups are almost surely
generated as a semigroup by the path of a random walk
on the group.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "random walks on groups, recurrence/transience,
semi-group",
}
@Article{Trevisan:2013:BRM,
author = "Dario Trevisan",
title = "{BV}-regularity for the {Malliavin} derivative of the
maximum of the {Wiener} process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "29:1--29:9",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2314",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2314",
abstract = "We show that, on the classical Wiener space, the
random variable $ M = \sup_{0 \le t \le T} W_t $ admits
a measure as second Malliavin derivative, whose total
variation measure is finite and singular w.r.t. the
Wiener measure.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "BV functions; Malliavin Calculus",
}
@Article{Daly:2013:CPA,
author = "Fraser Daly",
title = "Compound {Poisson} approximation with association or
negative association via {Stein}'s method",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "30:1--30:12",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2751",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2751",
abstract = "In this note we show how the properties of association
and negative association can be combined with Stein's
method for compound Poisson approximation. Applications
include $k$--runs in iid Bernoulli trials, an urn model
with urns of limited capacity and extremes of random
variables.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "(negative) association; Compound Poisson
approximation; extremes; runs; Stein's method; urn
model with overflow",
}
@Article{Trevisan:2013:ZNL,
author = "Dario Trevisan",
title = "Zero noise limits using local times",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "31:1--31:7",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2587",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2587",
abstract = "We consider a well-known family of SDEs with irregular
drifts and the correspondent zero noise limits. Using
(mollified) local times, we show which trajectories are
selected. The approach is completely probabilistic and
relies on elementary stochastic calculus only.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "local time; Peano phenomena; SDEs",
}
@Article{Valesin:2013:SAA,
author = "Daniel Valesin and Thomas Mountford",
title = "Supercriticality of an annealed approximation of
{Boolean} networks",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "32:1--32:12",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2479",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2479",
abstract = "We consider a model recently proposed by Chatterjee
and Durrett as an ``annealed approximation'' of boolean
networks, which are a class of cellular automata on a
random graph, as defined by S. Kauffman. The starting
point is a random directed graph on $n$ vertices; each
vertex has $r$ input vertices pointing to it. For the
model of Chatterjee and Durrett, a discrete time
threshold contact process is then considered on this
graph: at each instant, each vertex has probability $q$
of choosing to receive input; if it does, and if at
least one of its input vertices were in state 1 at the
previous instant, then it is labelled with a 1; in all
other cases, it is labelled with a 0. $r$ and $q$ are
kept fixed and $n$ is taken to infinity. Improving a
result of Chatterjee and Durrett, we show that if $ q r
> 1$ , then the time of persistence of activity of the
dynamics is exponential in $n$ .",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "boolean networks; random graphs; threshold contact
process",
}
@Article{Castell:2013:OSE,
author = "Fabienne Castell and Nadine Guillotin-Plantard and
Fran{\c{c}}oise P{\`e}ne and Bruno Schapira",
title = "On the one-sided exit problem for stable processes in
random scenery",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "33:1--33:7",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2444",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2444",
abstract = "We consider the one-sided exit problem for stable
L{\'e}vy process in random scenery, that is the
asymptotic behaviour for $T$ large of the
probability\par
$$ \mathbb {P} \Big [\sup_{t \in [0, T]} \Delta_t \leq
1 \Big] $$
where\par
$$ \Delta_t = \int_{\mathbb {R}} L_t(x) \, d W(x). $$
Here $ W = (W(x))_{x \in \mathbb {R}}$ is a two-sided
standard real Brownian motion and $ (L_t(x))_{x \in
\mathbb {R}, t \geq 0}$ the local time of a stable
L{\'e}vy process with index $ \alpha \in (1, 2]$,
independent from the process $W$. Our result confirms
some physicists prediction by Redner and Majumdar.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Stable process, Random scenery, First passage time,
One-sided barrier problem, One-sided exit problem,
Survival exponent.",
}
@Article{Aly:2013:PSC,
author = "Sidi Mohamed Ould Aly",
title = "Parameter sensitivity of {CIR} process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "34:1--34:6",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2035",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2035",
abstract = "We study the differentiability of the CIR process with
respect to its parameters. We give a stochastic
representation for these derivatives in terms of the
paths of V.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "CIR process; sensitivity",
}
@Article{Jonasson:2013:BIP,
author = "Johan Jonasson",
title = "The {BK} inequality for pivotal sampling {a.k.a.} the
{Srinivasan} sampling process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "35:1--35:6",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2045",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2045",
abstract = "The pivotal sampling algorithm, a.k.a. the Srinivasan
sampling process, is a simply described recursive
algorithm for sampling from a finite population a fixed
number of items such that each item is included in the
sample with a prescribed desired inclusion probability.
The algorithm has attracted quite some interest in
recent years due to the fact that despite its
simplicity, it has been shown to satisfy strong
properties of negative dependence, e.g. conditional
negative association. In this paper it is shown that
(tree-ordered) pivotal\slash Srinivasan sampling also
satisfies the BK inequality. This is done via a mapping
from increasing sets of samples to sets of match
sequences and an application of the van den
Berg-Kesten-Reimer inequality. The result is one of
only very few non-trivial situations where the BK
inequality is known to hold.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Srinivasan sampling, negative association, Reimer's
inequality",
}
@Article{Klicnarova:2013:ZWC,
author = "Jana Klicnarova and Dalibor Volny",
title = "On {Zhao--Woodroofe}'s condition for martingale
approximation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "36:1--36:8",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2780",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2780",
abstract = "The Zhao--Woodroofe condition is a necessary and
sufficient condition for the existence of a martingale
approximation of a causal stationary process. Here, a
nonadapted version is given and the convergence of
Cesaro averages is replaced by a convergence of a
subsequence. The nonadapted version is of a different
form than in other cases, e.g. of Wu--Woodroofe or
Maxwell--Woodroofe conditions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "martingale approximation; nonadapted version;
stationary process",
}
@Article{Marinucci:2013:MSC,
author = "Domenico Marinucci and Giovanni Peccati",
title = "Mean-Square continuity on homogeneous spaces of
compact groups",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "37:1--37:10",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2400",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2400",
abstract = "We show that any finite-variance, isotropic random
field on a compact group is necessarily mean-square
continuous, under standard measurability assumptions.
The result extends to isotropic random fields defined
on homogeneous spaces where the group acts
continuously.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Isotropy; Mean-Square Continuity; Random Processes",
}
@Article{Swart:2013:NIN,
author = "Jan Swart",
title = "Noninvadability implies noncoexistence for a class of
cancellative systems",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "38:1--38:12",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2471",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2471",
abstract = "There exist a number of results proving that for
certain classes of interacting particle systems in
population genetics, mutual invadability of types
implies coexistence. In this paper we prove a sort of
converse statement for a class of one-dimensional
cancellative systems that are used to model balancing
selection. We say that a model exhibits strong
interface tightness if started from a configuration
where to the left of the origin all sites are of one
type and to the right of the origin all sites are of
the other type, the configuration as seen from the
interface has an invariant law in which the number of
sites where both types meet has finite expectation. We
prove that this implies noncoexistence, i.e., all
invariant laws of the process are concentrated on the
constant configurations. The proof is based on special
relations between dual and interface models that hold
for a large class of one-dimensional cancellative
systems and that are proved here for the first time.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "affine voter model; annihilation; balancing selection;
branching; Cancellative system; duality, coexistence;
interface tightness; Neuhauser-Pacala model; parity
preservation; rebellious voter model",
}
@Article{Sokol:2013:ONT,
author = "Alexander Sokol",
title = "Optimal Novikov-type criteria for local martingales
with jumps",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "39:1--39:8",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2312",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2312",
abstract = "We consider cadlag local martingales M with initial
value zero and jumps larger than a for some a larger
than or equal to -1, and prove Novikov-type criteria
for an exponential local martingale to be a uniformly
integrable martingale. We obtain criteria using both
the quadratic variation and the predictable quadratic
variation. We prove optimality of the coefficients in
the criteria. As a corollary, we obtain a verbatim
extension of the classical Novikov criterion for
continuous local martingales to the case of local
martingales with initial value zero and nonnegative
jumps.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Martingale, Exponential martingale, Uniform
integrability, Novikov, Optimal, Poisson process",
}
@Article{Lampert:2013:MSR,
author = "Amichai Lampert and Assaf Shapira",
title = "On maximizing the speed of a random walk in fixed
environments",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "40:1--40:9",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2431",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2431",
abstract = "We consider a random walk in a fixed $ \mathbb {Z} $
environment composed of two point types: $q$-drifts (in
which the probability to move to the right is $q$, and
$ 1 - q$ to the left) and $p$-drifts, where $ \frac
{1}{2} < q < p$. We study the expected hitting time of
a random walk at $N$ given the number of $p$-drifts in
the interval $ [1, N - 1]$, and find that this time is
minimized asymptotically by equally spaced
$p$-drifts.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Environment; Random Walk; Speed",
}
@Article{Bertoin:2013:PJI,
author = "Jean Bertoin and Marc Yor",
title = "Pure jump increasing processes and the change of
variables formula",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "41:1--41:7",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2700",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2700",
abstract = "Given an increasing process $ (A_t)_{t \geq 0} $, we
characterize the right continuous non-decreasing
functions $ f : \mathbb {R}_+ \to \mathbb {R}_+ $ that
map $A$ to a pure jump process. As an example of
application, we show for instance that functions with
bounded variations belong to the domain of the extended
generator of any subordinator with no drift and
infinite L{\'e}vy measure.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Pure jump process, increasing process, change of
variables, subordinator, extended infinitesimal
generator",
}
@Article{Hackmann:2013:NSR,
author = "Daniel Hackmann and Alexey Kuznetsov",
title = "A note on the series representation for the density of
the supremum of a stable process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "42:1--42:5",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2757",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2757",
abstract = "An absolutely convergent double series representation
for the density of the supremum of $ \alpha $-stable
L{\'e}vy process was obtained by Hubalek and Kuznetsov
for almost all irrational $ \alpha $. This result
cannot be made stronger in the following sense: the
series does not converge absolutely when $ \alpha $
belongs to a certain subset of irrational numbers of
Lebesgue measure zero. Our main result in this note
shows that for every irrational $ \alpha $ there is a
way to rearrange the terms of the double series, so
that it converges to the density of the supremum. We
show how one can establish this stronger result by
introducing a simple yet non-trivial modification in
the original proof of Hubalek and Kuznetsov.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "stable processes, supremum, Mellin transform,
continued fractions",
}
@Article{Alexander:2013:CRW,
author = "Kenneth Alexander",
title = "Controlled random walk with a target site",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "43:1--43:6",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2763",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2763",
abstract = "We consider a symmetric simple random walk $ \{ W_i \}
$ on $ \mathbb {Z}^d, d = 1, 2 $, in which the walker
may choose to stand still for a limited time. The time
horizon is $n$, the maximum consecutive time steps
which can be spent standing still is $ m_n$ and the
goal is to maximize $ \mathbb {P}(W_n = 0)$. We show
that for $ d = 1$, if $ m_n \gg (\log n)^{2 + \gamma }$
for some $ \gamma > 0$, there is a strategy for each
$n$ yielding $ \mathbb {P}(W_n = 0) \to 1$. For $ d =
2$, if $ m_n \gg n^\epsilon $ for some $ \epsilon > 0$
then there are strategies yielding $ \liminf_n \mathbb
{P}(W_n = 0) > 0$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "random walk, stochastic control",
}
@Article{Rio:2013:MCI,
author = "Emmanuel Rio",
title = "On {McDiarmid}'s concentration inequality",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "44:1--44:11",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2659",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2659",
abstract = "In this paper we improve the rate function in the
McDiarmid concentration inequality for separately
Lipschitz functions of independent random variables. In
particular the rate function tends to infinity at the
boundary. We also prove that in some cases the usual
normalization factor is not adequate and may be
improved.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "McDiarmid inequality, Concentration inequality,
Hoeffding inequality, Vajda's tight lower bound",
}
@Article{Cui:2013:ABN,
author = "Jing Cui and Litan Yan",
title = "Asymptotic behavior for neutral stochastic partial
differential equations with infinite delays",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "45:1--45:12",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2858",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2858",
abstract = "This paper is concerned with the existence and
asymptotic behavior of mild solutions to a class of
non-linear neutral stochastic partial differential
equations with infinite delays. By applying fixed point
principle, we present sufficient conditions to ensure
that the mild solutions are exponentially stable in $p$
th-moment ($ p \geq 2$) and almost surely exponentially
stable. An example is provided to illustrate the
effectiveness of the proposed result.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "exponential stability; infinite delay; Neutral
stochastic partial differential equations",
}
@Article{Spinu:2013:PLB,
author = "Florin Spinu",
title = "The probability law of the {Brownian} motion
normalized by its range",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "46:1--46:8",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2568",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2568",
abstract = "In the present paper we deduce explicit formulas for
the probability laws of the quotients $ X_t / R_t $ and
$ m_t / R_t $, where $ X_t $ is the standard Brownian
motion and $ m_t $, $ M_t $, $ R_t $ are its running
minimum, maximum and range, respectively. The
computation makes use of standard techniques from
analytic number theory and the theory of the Hurwitz
zeta function.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion, Hurwitz zeta",
}
@Article{Sabanis:2013:NTE,
author = "Sotirios Sabanis",
title = "A note on tamed {Euler} approximations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "47:1--47:10",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2824",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2824",
abstract = "Strong convergence results on tamed Euler schemes,
which approximate stochastic differential equations
with superlinearly growing drift coefficients that are
locally one-sided Lipschitz continuous, are presented
in this article. The diffusion coefficients are assumed
to be locally Lipschitz continuous and have at most
linear growth. Furthermore, the classical rate of
convergence, i.e. one-half, for such schemes is
recovered when the local Lipschitz continuity
assumptions are replaced by global and, in addition, it
is assumed that the drift coefficients satisfy
polynomial Lipschitz continuity.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Euler approximations; local Lipschitz condition;
monotonicity condition.; rate of convergence",
}
@Article{Yen:2013:IVM,
author = "Ju-Yi Yen and Marc Yor",
title = "Illustration of various methods for solving partly
{Skorokhod}'s embedding problem",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "48:1--48:5",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2178",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2178",
abstract = "We show that excursion theory and Az{\'e}ma's
exponential result allow to solve partly Skorokhod's
embedding problem.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Az\'\{e\}ma exponential result; excursion; Skorokhod
embedding",
}
@Article{Rudolf:2013:PHR,
author = "Daniel Rudolf and Mario Ullrich",
title = "Positivity of hit-and-run and related algorithms",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "49:1--49:8",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2507",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2507",
abstract = "We prove positivity of the Markov operators that
correspond to the hit-and-run algorithm, random scan
Gibbs sampler, slice sampler and Metropolis algorithm
with positive proposal. In particular, the results show
that it is not necessary to consider the lazy versions
of these Markov chains. The proof relies on a well
known lemma which relates the positivity of the product
$ M T M^* $, for some operators $M$ and $T$, to the
positivity of $T$. It remains to find that kind of
representation of the Markov operator with a positive
operator $T$.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "hit-and-run; lazy; Metropolis; positivity; Spectral
gap",
}
@Article{Duminil-Copin:2013:CID,
author = "Hugo Duminil-Copin and Cyrille Lucas and Ariel Yadin
and Amir Yehudayoff",
title = "Containing internal diffusion limited aggregation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "50:1--50:8",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2862",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2862",
abstract = "Internal Diffusion Limited Aggregation (IDLA) is a
model that describes the growth of a random aggregate
of particles from the inside out. Shellef proved that
IDLA processes on supercritical percolation clusters of
integer-lattices fill Euclidean balls, with high
probability. In this article, we complete the picture
and prove a limit-shape theorem for IDLA on such
percolation clusters, by providing the corresponding
upper bound.\par
The technique to prove upper bounds is new and robust:
it only requires the existence of a ``good'' lower
bound. Specifically, this way of proving upper bounds
on IDLA clusters is more suitable for random
environments than previous ways, since it does not
harness harmonic measure estimates.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "IDLA, Random Walk, Percolation",
}
@Article{Wainrib:2013:DAP,
author = "Gilles Wainrib",
title = "Double averaging principle for periodically forced
stochastic slow-fast systems",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "51:1--51:12",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-1975",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/1975",
abstract = "This paper is devoted to obtaining an averaging
principle for systems of slow-fast stochastic
differential equations, where the fast variable drift
is periodically modulated on a fast time-scale. The
approach developed here combines probabilistic methods
with a recent analytical result on long-time behavior
for second order elliptic equations with time-periodic
coefficients.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "averaging principle; inhomogeneous Markov process;
periodic averaging; slow-fast; stochastic differential
equation",
}
@Article{Tsirelson:2013:URT,
author = "Boris Tsirelson",
title = "From uniform renewal theorem to uniform large and
moderate deviations for renewal-reward processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "52:1--52:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2719",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2719",
abstract = "A uniform key renewal theorem is deduced from the
uniform Blackwell's renewal theorem. A uniform LDP
(large deviation principle) for renewal-reward
processes is obtained, and MDP (moderate deviation
principle) is deduced under conditions much weaker than
existence of exponential moments.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "moderate deviation; renewal-reward; uniform renewal
theorem",
}
@Article{Friedland:2013:SOR,
author = "Omer Friedland and Ohad Giladi",
title = "A simple observation on random matrices with
continuous diagonal entries",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "53:1--53:7",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2633",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2633",
abstract = "Let $T$ be an $ n \times n$ random matrix, such that
each diagonal entry $ T_{i, i}$ is a continuous random
variable, independent from all the other entries of
$T$. Then for every $ n \times n$ matrix $A$ and every
$ t \ge 0$ \par
$$ \mathbb {P} \Big [| \det (A + T)|^{1 / n} \le t
\Big] \le 2 b n t, $$
where $ b > 0$ is a uniform upper bound on the
densities of $ T_{i, i}$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Rio:2013:EHA,
author = "Emmanuel Rio",
title = "Extensions of the {Hoeffding--Azuma} inequalities",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "54:1--54:6",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2690",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2690",
abstract = "In this paper we give extensions of the
Hoeffding--Azuma inequalities for weighted sums of
uniformly bounded martingale differences.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Hoeffding inequality, Azuma inequality, Discrete time
martingales, McDiarmid inequality",
}
@Article{Peled:2013:GLF,
author = "Ron Peled and Wojciech Samotij and Amir Yehudayoff",
title = "Grounded {Lipschitz} functions on trees are typically
flat",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "55:1--55:9",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2796",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2796",
abstract = "A grounded $M$-Lipschitz function on a rooted $d$-ary
tree is an integer valued map on the vertices that
changes by at most $M$ along edges and attains the
value zero on the leaves. We study the behavior of such
functions, specifically, their typical value at the
root $ v_0$ of the tree. We prove that the probability
that the value of a uniformly chosen random function at
$ v_0$ is more than $ M + t$ is doubly-exponentially
small in $t$. We also show a similar bound for
continuous (real-valued) grounded Lipschitz
functions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random Lipschitz functions; rooted trees",
}
@Article{Laurent:2013:SNN,
author = "St{\'e}phane Laurent",
title = "Standardness and nonstandardness of next-jump time
filtrations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "56:1--56:11",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2766",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2766",
abstract = "The value of the next-jump time process at each time
is the date of its the next jump. We characterize the
standardness of the filtration generated by this
process in terms of the asymptotic behavior at $ n = -
\infty $ of the probability that the process jumps at
time $n$. In the case when the filtration is not
standard we characterize the standardness of its
extracted filtrations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Cosy filtration; Standard filtration",
}
@Article{Labbe:2013:QSD,
author = "Cyril Labb{\'e}",
title = "Quasi-stationary distributions associated with
explosive {CSBP}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "57:1--57:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2508",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2508",
abstract = "We characterize all the quasi-stationary distributions
and the Q process associated with a continuous state
branching process that explodes in finite time. We also
provide a rescaling for the continuous state branching
process conditioned on non-explosion when the branching
mechanism is regularly varying at 0.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Continuous-state branching process; Drift; Q-process;
Quasi-stationary distribution; Regular variation",
}
@Article{Angel:2013:AC,
author = "Omer Angel and Alexander Holroyd and James Martin and
Peter Winkler and David Wilson",
title = "Avoidance Coupling",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "58:1--58:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2275",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2275",
abstract = "We examine the question of whether a collection of
random walks on a graph can be coupled so that they
never collide. In particular, we show that on the
complete graph on n vertices, with or without loops,
there is a Markovian coupling keeping apart Omega(n/log
n) random walks, taking turns to move in discrete
time.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "coupling, coloring",
}
@Article{Ostrovsky:2013:TBB,
author = "Dmitry Ostrovsky",
title = "Theory of {Barnes} {Beta} distributions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "59:1--59:16",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2445",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2445",
abstract = "A new family of probability distributions $ \beta_{M,
N}, $ $ M = 0 \cdots N, $ $ N \in \mathbb {N} $ on the
unit interval $ (0, 1] $ is defined by the Mellin
transform. The Mellin transform of $ \beta_{M, N} $ is
characterized in terms of products of ratios of Barnes
multiple gamma functions, shown to satisfy a functional
equation, and a Shintani-type infinite product
factorization. The distribution $ \log \beta_{M, N} $
is infinitely divisible. If $ M < N, $ $ - \log
\beta_{M, N} $ is compound Poisson, if $ M = N, $ $
\log \beta_{M, N} $ is absolutely continuous. The
integral moments of $ \beta_{M, N} $ are expressed as
Selberg-type products of multiple gamma functions. The
asymptotic behavior of the Mellin transform is derived
and used to prove an inequality involving multiple
gamma functions and establish positivity of a class of
alternating power series. For application, the Selberg
integral is interpreted probabilistically as a
transformation of $ \beta_{1, 1} $ into a product of $
\beta^{-1}_{2, 2}s. $",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Infinite divisibility; Mellin transform; Multiple
gamma function; Selberg Integral",
}
@Article{Chleboun:2013:MTB,
author = "Paul Chleboun and Fabio Martinelli",
title = "Mixing time bounds for oriented kinetically
constrained spin models",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "60:1--60:9",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2516",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2516",
abstract = "We analyze the mixing time of a class of oriented
kinetically constrained spin models (KCMs) on a
d-dimensional lattice of n sites. A typical example is
the North-East model, a 0-1 spin system on the
two-dimensional integer lattice that evolves according
to the following rule: whenever a site's southerly and
westerly nearest neighbours have spin 0, with rate one
it resets its own spin by tossing a p-coin, at all
other times its spin remains frozen. Such models are
very popular in statistical physics because, in spite
of their simplicity, they display some of the key
features of the dynamics of real glasses. We prove that
the mixing time is O(n log n) whenever the relaxation
time is O(1). Our study was motivated by the
\textquotedblleft shape\textquotedblright conjecture
put forward by G. Kordzakhia and S.P . Lalley.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "North-East model, kinetically constrained spin models,
mixing time",
}
@Article{Moon:2013:HBV,
author = "Hee-Jin Moon and Chang-Ho Han and Yong-Kab Choi",
title = "How big are the $ l^\infty $-valued random fields?",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "61:1--61:9",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2417",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2417",
abstract = "In this paper we establish path properties and a
generalized uniform law of the iterated logarithm (LIL)
for strictly stationary and linearly positive quadrant
dependent (LPQD) or linearly negative quadrant
dependent (LNQD) random fields taking values in $
l^\infty $-space.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "linearly positive quadrant dependence, linearly
negative quadrant dependence, stationary random field,
law of the iterated logarithm.",
}
@Article{Dassios:2013:ESH,
author = "Angelos Dassios and Hongbiao Zhao",
title = "Exact simulation of {Hawkes} process with
exponentially decaying intensity",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "62:1--62:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2717",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2717",
abstract = "We introduce a numerically efficient simulation
algorithm for Hawkes process with exponentially
decaying intensity, a special case of general Hawkes
process that is most widely implemented in practice.
This computational method is able to exactly generate
the point process and intensity process, by sampling
interarrival times directly via the underlying analytic
distribution functions without numerical inverse, and
hence avoids simulating intensity paths and introducing
discretisation bias. Moreover, it is flexible to
generate points with either stationary or
non-stationary intensity, starting from any arbitrary
time with any arbitrary initial intensity. It is also
straightforward to implement, and can easily extend to
multi-dimensional versions, for further applications in
modelling contagion risk or clustering arrival of
events in finance, insurance, economics and many other
fields. Simulation algorithms for one dimension and
multi-dimension are represented, with numerical
examples of univariate and bivariate processes provided
as illustrations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Contagion risk; Exact simulation; Hawkes process;
Hawkes process with exponentially decaying intensity;
Monte Carlo simulation.; Self-exciting point process;
Stochastic intensity model",
}
@Article{Yang:2013:SPG,
author = "Zhe Yang and Robert Elliott",
title = "Some properties of generalized anticipated backward
stochastic differential equations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "63:1--63:10",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2415",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2415",
abstract = "In this paper, after recalling the definition of
generalized anticipated backward stochastic
differential equations (generalized anticipated BSDEs
for short) and the existence and uniqueness theorem for
their solutions, we show there is a duality between
them and stochastic differential delay equations. We
then provide a continuous dependence property for their
solutions with respect to the parameters and finally
establish a comparison result for the solutions of
these equations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "comparison theorem; continuous dependence property;
duality; Generalized anticipated BSDEs",
}
@Article{Aman:2013:RTS,
author = "Auguste Aman and Abouo Elouaflin and Mamadou Diop",
title = "Representation theorems for {SPDEs} via backward
doubly",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "64:1--64:15",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2223",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2223",
abstract = "In this paper we establish a probabilistic
representation for the spatial gradient of the
viscosity solution to a quasilinear parabolic
stochastic partial differential equations(SPDE, for
short) in the spirit of the Feynman--Kac formula,
without using the derivatives of the coefficients of
the corresponding backward doubly stochastic
differential equations (FBDSDE, for short).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Backward doubly SDEs, stochastic partial differential
equation, stochastic viscosity",
}
@Article{Mentemeier:2013:NKC,
author = "Sebastian Mentemeier",
title = "A note on {Kesten}'s {Choquet--Deny} lemma",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "65:1--65:7",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2629",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See erratum \cite{Mentemeier:2014:ENK}.",
URL = "http://ecp.ejpecp.org/article/view/2629",
abstract = "Let $ d > 1 $ and $ (A_n)_{n \in \mathbb {N}} $ be a
sequence of independent identically distributed random
matrices with nonnegative entries. This induces a
Markov chain $ M_n = A_n M_{n - 1} $ on the cone $
\mathbb {R}^d_{\ge } \setminus \{ 0 \} = \mathbb
{S}_\ge \times \mathbb {R}_> $. We study harmonic
functions of this Markov chain. In particular, it is
shown that all bounded harmonic functions in $ \mathcal
{C}_b(\mathbb {S}_\ge) \otimes \mathcal {C}_b(\mathbb
{R}_>) $ are constant. The idea of the proof is
originally due to Kesten [Renewal theory for
functionals of a Markov chain with general state space,
Ann. Prob. 2 (1974), 355 - 386], but is considerably
shortened here. A similar result for invertible
matrices is given as well.\par
{\bf There is an erratum in
\url{https://doi.org/10.1214/ECP.v19-3381} ECP volume
{\bf 19} paper 20 (2014).}",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Choquet-Deny Lemma, Markov Random Walks, Products of
Random Matrices",
}
@Article{Dzindzalieta:2013:ELF,
author = "Dainius Dzindzalieta",
title = "Extremal {Lipschitz} functions in the deviation
inequalities from the mean",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "66:1--66:5",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2814",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2814",
abstract = "We obtain an optimal deviation from the mean upper
bound $ D(x) = \sup \{ \mu \{ f - \mathbb {E}_{\mu } f
\geq x \} : f \in \mathcal {F}, x \in \mathbb {R} \} $
where $ \mathcal {F} $ is the class of the integrable,
Lipschitz functions on probability metric (product)
spaces. As corollaries we get exact bounds for
Euclidean unit sphere $ S^{n - 1} $ with a geodesic
distance and a normalized Haar measure, for $ \mathbb
{R}^n $ equipped with a Gaussian measure and for the
multidimensional cube, rectangle, torus or Diamond
graph equipped with uniform measure and Hamming
distance. We also prove that in general probability
metric spaces the $ \sup $ is achieved on a family of
distance functions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Gaussian, vertex isoperimetric, deviation from the
mean, inequalities, Hamming, probability metric space",
}
@Article{Stucki:2013:CPG,
author = "Kaspar Stucki",
title = "Continuum percolation for {Gibbs} point processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "67:1--67:10",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2837",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2837",
abstract = "We consider percolation properties of the Boolean
model generated by a Gibbs point process and balls with
deterministic radius. We show that for a large class of
Gibbs point processes there exists a critical activity,
such that percolation occurs a.s. above criticality.
For locally stable Gibbs point processes we show a
converse result, i.e. they do not percolate a.s. at low
activity.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Boolean model; Conditional intensity; Gibbs point
process; Percolation",
}
@Article{Carmona:2013:MFF,
author = "Ren{\'e} Carmona and Fran{\c{c}}ois Delarue",
title = "Mean field forward-backward stochastic differential
equations",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "68:1--68:15",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2446",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2446",
abstract = "The purpose of this note is to provide an existence
result for the solution of fully coupled Forward
Backward Stochastic Differential Equations (FBSDEs) of
the mean field type. These equations occur in the study
of mean field games and the optimal control of dynamics
of the McKean Vlasov type.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "FBSDEs, Mean Field Interactions",
}
@Article{Basak:2013:LSD,
author = "Anirban Basak and Amir Dembo",
title = "Limiting spectral distribution of sum of unitary and
orthogonal matrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "69:1--69:19",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2466",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2466",
abstract = "We show that the empirical eigenvalue measure for sum
of $d$ independent Haar distributed $n$-dimensional
unitary matrices, converge for $ n \rightarrow \infty $
to the Brown measure of the free sum of $d$ Haar
unitary operators. The same applies for independent
Haar distributed $n$-dimensional orthogonal matrices.
As a byproduct of our approach, we relax the
requirement of uniformly bounded imaginary part of
Stieltjes transform of $ T_n$ that is made in
[Guionnet, Krishnapur, Zeitouni; Theorem 1].",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Random matrices, limiting spectral distribution, Haar
measure, Brown measure, free convolution, Stieltjes
transform, Schwinger-Dyson equation.",
}
@Article{Dohmen:2013:LBP,
author = "Klaus Dohmen",
title = "Lower bounds for the probability of a union via
chordal graphs",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "70:1--70:4",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2357",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2357",
abstract = "We establish new Bonferroni-type lower bounds for the
probability of a union of finitely many events where
the selection of intersections in the estimates is
determined by the clique complex of a chordal graph.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bonferroni inequality; chordal graph; clique complex;
independence number",
}
@Article{Sandric:2013:TCC,
author = "Nikola Sandri{\'c}",
title = "A transience condition for a class of one-dimensional
symmetric {L{\'e}vy} processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "71:1--71:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2802",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2802",
abstract = "In this paper, we give a sufficient condition for the
transience for a class of one dimensional symmetric
L{\'e}vy processes. More precisely, we prove that a one
dimensional symmetric L{\'e}vy process with the
L{\'e}vy measure $ \nu (d y) = f(y)d y $ or $ \nu (\{ n
\}) = p_n $, where the density function $ f(y) $ is
such that $ f(y) > 0 $ a.e. and the sequence $ \{ p_n
\}_{n \geq 1} $ is such that $ p_n > 0 $ for all $ n
\geq 1 $, is transient if\par
$$ \int_1^{\infty } \frac {dy}{y^3f(y)} < \infty \quad
\mbox {or} \quad \sum_{n = 1}^{\infty } \frac
{1}{n^3p_n} < \infty . $$
Similarly, we derive an analogous transience condition
for one-dimensional symmetric random walks with
continuous and discrete jumps.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "characteristics of a semimartingale; electrical
network; L{\'e}vy measure; L{\'e}vy process; random
walk; recurrence; transience",
}
@Article{Foucart:2013:ISW,
author = "Cl{\'e}ment Foucart",
title = "The impact of selection in the {$ \Lambda
$--Wright--Fisher} model",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "72:1--72:10",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2838",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
note = "See erratum \cite{Foucart:2014:EIS}.",
URL = "http://ecp.ejpecp.org/article/view/2838",
abstract = "The purpose of this article is to study some
asymptotic properties of the $ \Lambda $-Wright--Fisher
process with selection. This process represents the
frequency of a disadvantaged allele. The resampling
mechanism is governed by a finite measure $ \Lambda $
on $ [0, 1]$ and selection by a parameter $ \alpha $.
When the measure $ \Lambda $ obeys $ \int_0^1 - \log (1
- x)x^{-2} \Lambda (d x) < \infty $, some particular
behaviour in the frequency of the allele can occur. The
selection coefficient $ \alpha $ may be large enough to
override the random genetic drift. In other words, for
certain selection pressure, the disadvantaged allele
will vanish asymptotically with probability one. This
phenomenon cannot occur in the classical Wright--Fisher
diffusion. We study the dual process of the $ \Lambda
$-Wright--Fisher process with selection and prove this
result through martingale arguments.\par
\url{https://doi.org/10.1214/ECP.v19-3351} There is an
Erratum in ECP volume {\bf 19} paper 15 (2014).",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Crane:2013:CMB,
author = "Harry Crane",
title = "Consistent {Markov} branching trees with discrete edge
lengths",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "73:1--73:14",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2872",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2872",
abstract = "We study consistent collections of random
fragmentation trees with random integer-valued edge
lengths. We prove several equivalent necessary and
sufficient conditions under which Geometrically
distributed edge lengths can be consistently assigned
to a Markov branching tree. Among these conditions is a
characterization by a unique probability measure, which
plays a role similar to the dislocation measure for
homogeneous fragmentation processes. We discuss this
and other connections to previous work on Markov
branching trees and homogeneous fragmentation
processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "dislocation measure; exchangeable random partition;
homogeneous fragmentation process; Markov branching
model; random tree; sampling consistency; splitting
rule; weighted tree",
}
@Article{Nualart:2013:CLT,
author = "David Nualart and Fangjun Xu",
title = "Central limit theorem for an additive functional of
the fractional {Brownian} motion {II}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "74:1--74:10",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2761",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2761",
abstract = "We prove a central limit theorem for an additive
functional of the $d$-dimensional fractional Brownian
motion with Hurst index $ H \in (\frac {1}{d + 2},
\frac {1}{d})$, using the method of moments, extending
the result by Papanicolaou, Stroock and Varadhan in the
case of the standard Brownian motion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "central limit theorem; fractional Brownian motion;
local time; method of moments",
}
@Article{Kumagai:2013:FMD,
author = "Takashi Kumagai and Ofer Zeitouni",
title = "Fluctuations of maxima of discrete {Gaussian} free
fields on a class of recurrent graphs",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "75:1--75:12",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2632",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2632",
abstract = "We provide conditions that ensure that the maximum of
the Gaussian free field on a sequence of graphs
fluctuates at the same order as the field at the point
of maximal standard deviation; under these conditions,
the expectation of the maximum is of the same order as
the maximal standard deviation. In particular, on a
sequence of such graphs the recentered maximum is not
tight, similarly to the situation in $ \mathbb {Z} $
but in contrast with the situation in $ \mathbb {Z}^2
$. We show that our conditions cover a large class of
{"fractal"} graphs.\par",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "fractal graphs; Gaussian free field",
}
@Article{Caravenna:2013:GSI,
author = "Francesco Caravenna and Frank den Hollander",
title = "A general smoothing inequality for disordered
polymers",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "76:1--76:15",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2874",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2874",
abstract = "This note sharpens the smoothing inequality of
Giacomin and Toninelli for disordered polymers. This
inequality is shown to be valid for any disorder
distribution with locally finite exponential moments,
and to provide an asymptotically sharp constant for
weak disorder. A key tool in the proof is an estimate
that compares the effect on the free energy of tilting,
respectively, shifting the disorder distribution. This
estimate holds in large generality (way beyond
disordered polymers) and is of independent interest.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Smoothing Inequality, Disordered Polymer, Pinning
Model, Copolymer Model, Disorder Tilt, Disorder Shift",
}
@Article{Cannings:2013:RWA,
author = "Chris Cannings and Jonathan Jordan",
title = "Random walk attachment graphs",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "77:1--77:5",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2518",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2518",
abstract = "We consider the random walk attachment graph
introduced by Saram{\"a}ki and Kaski and proposed as a
mechanism to explain how behaviour similar to
preferential attachment may appear requiring only local
knowledge. We show that if the length of the random
walk is fixed then the resulting graphs can have
properties significantly different from those of
preferential attachment graphs, and in particular that
in the case where the random walks are of length 1 and
each new vertex attaches to a single existing vertex
the proportion of vertices which have degree 1 tends to
1, in contrast to preferential attachment models.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "preferential attachment; random graphs; random walk",
}
@Article{Meckes:2013:SMP,
author = "Elizabeth Meckes and Mark Meckes",
title = "Spectral measures of powers of random matrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "78:1--78:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2551",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2551",
abstract = "This paper considers the empirical spectral measure of
a power of a random matrix drawn uniformly from one of
the compact classical matrix groups. We give sharp
bounds on the $ L_p$-Wasserstein distances between this
empirical measure and the uniform measure on the
circle, which show a smooth transition in behavior when
the power increases and yield rates on almost sure
convergence when the dimension grows. Along the way, we
prove the sharp logarithmic Sobolev inequality on the
unitary group.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "logarithmic Sobolev inequality; spectral measure;
Uniform random matrices; Wasserstein distance",
}
@Article{He:2013:NSL,
author = "Hui He and Nana Luan",
title = "A note on the scaling limits of contour functions of
{Galton--Watson} trees",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "79:1--79:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2781",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2781",
abstract = "Recently, Abraham and Delmas constructed the
distributions of super-critical L{\'e}vy trees
truncated at a fixed height by connecting
super-critical L{\'e}vy trees to (sub)critical L{\'e}vy
trees via a martingale transformation. A similar
relationship also holds for discrete Galton--Watson
trees. In this work, using the existing works on the
convergence of contour functions of (sub)critical
trees, we prove that the contour functions of truncated
super critical Galton--Watson trees converge weakly to
the distributions constructed by Abraham and Delmas.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Branching processes; contour functions; Galton--Watson
trees; L{\'e}vy trees; scaling limit",
}
@Article{Berti:2013:SRT,
author = "Patrizia Berti and Luca Pratelli and Pietro Rigo",
title = "A {Skorohod} representation theorem without
separability",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "80:1--80:12",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2793",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2793",
abstract = "Let $ (S, d) $ be a metric space, $ \mathcal {G} $ a $
\sigma $-field on $S$ and $ (\mu_n : n \geq 0)$ a
sequence of probabilities on $ \mathcal {G}$. Suppose $
\mathcal {G}$ countably generated, the map $ (x, y)
\mapsto d(x, y)$ measurable with respect to $ \mathcal
{G} \otimes \mathcal {G}$, and $ \mu_n$ perfect for $ n
> 0$. Say that $ (\mu_n)$ has a Skorohod representation
if, on some probability space, there are random
variables $ X_n$ such that\par
\begin{equation*} X_n\sim\mu_n\text{ for all n}\geq
0\quad\text{and}\quad d(X_n,
X_0)\overset{P}\longrightarrow 0.
\end{equation*}\par
It is shown that $ (\mu_n)$ has a Skorohod
representation if and only if\par
\begin{equation*} \lim_n\, \sup_f\,
\left|\mu_n(f)-\mu_0(f)\right|=0,
\end{equation*}\par
where $ \sup $ is over those $ f : S \rightarrow [ - 1,
1]$ which are $ \mathcal {G}$-universally measurable
and satisfy $ \left |f(x) - f(y) \right | \leq 1 \wedge
d(x, y)$. An useful consequence is that Skorohod
representations are preserved under mixtures. The
result applies even if $ \mu_0$ fails to be
$d$-separable. Some possible applications are given as
well.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Convergence of probability measures, Perfect
probability measure, Separable probability measure,
Skorohod representation theorem, Uniform distance",
}
@Article{Nualart:2013:JCA,
author = "David Nualart and Jason Swanson",
title = "Joint convergence along different subsequences of the
signed cubic variation of fractional {Brownian} motion
{II}",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "81:1--81:11",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2840",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2840",
abstract = "The purpose of this paper is to provide a complete
description the convergence in distribution of two
subsequences of the signed cubic variation of the
fractional Brownian motion with Hurst parameter $ H = 1
/ 6 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Fractional Brownian motion, cubic variation,
convergence in law",
}
@Article{Rudelson:2013:HWI,
author = "Mark Rudelson and Roman Vershynin",
title = "{Hanson--Wright} inequality and sub-{Gaussian}
concentration",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "82:1--82:9",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2865",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2865",
abstract = "In this expository note, we give a modern proof of
Hanson--Wright inequality for quadratic forms in
sub-Gaussian random variables. We deduce a useful
concentration inequality for sub-Gaussian random
vectors. Two examples are given to illustrate these
results: a concentration of distances between random
vectors and subspaces, and a bound on the norms of
products of random and deterministic matrices.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "subGaussian random variables, measure concentration",
}
@Article{Venker:2013:PSR,
author = "Martin Venker",
title = "Particle systems with repulsion exponent $ \beta $ and
random matrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "83:1--83:12",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2864",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2864",
abstract = "We consider a class of particle systems generalizing
the $ \beta $ Ensembles from random matrix theory. In
these new ensembles, particles experience repulsion of
power $ \beta > 0 $ when getting close, which is the
same as in the $ \beta $-Ensembles. For distances
larger than zero, the interaction is allowed to differ
from those present for random eigenvalues. We show that
the local bulk correlations of the $ \beta $-Ensembles,
universal in random matrix theory, also appear in these
new ensembles.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "$\beta$-Ensembles; Random Matrices; Repulsion;
Universality",
}
@Article{Hu:2013:NDS,
author = "Yaozhong Hu and Fei Lu and David Nualart",
title = "Non-degeneracy of some {Sobolev} Pseudo-norms of
fractional {Brownian} motion",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "84:1--84:8",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2986",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2986",
abstract = "Applying an upper bound estimate for $ L^2 $ small
ball probability for fractional Brownian motion (fBm),
we prove the non degeneracy of some Sobolev
pseudo-norms of fBm.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "fractional Brownian motion; Malliavin calculus;
non-degeneracy; small deviation (small ball
probability).",
}
@Article{Guillotin-Plantard:2013:QLD,
author = "Nadine Guillotin-Plantard and Yueyun Hu and Bruno
Schapira",
title = "The quenched limiting distributions of a
one-dimensional random walk in random scenery",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "85:1--85:7",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2918",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2918",
abstract = "For a one-dimensional random walk in random scenery
(RWRS) on Z, we determine its quenched weak limits by
applying Strassen's functional law of iterated
logarithm. As a consequence, conditioned on the random
scenery, the one dimensional RWRS does not converge in
law, in contrast with the multi-dimensional case.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Brownian motion in Brownian Scenery; Law of the
iterated logarithm; Random walk in random scenery;
Strong approximation; Weak limit theorem",
}
@Article{Angel:2013:LLU,
author = "Omer Angel and Guillaume Chapuy and Nicolas Curien and
Gourab Ray",
title = "The local limit of unicellular maps in high genus",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "86:1--86:8",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-3037",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/3037",
abstract = "We show that the local limit of unicellular maps whose
genus is proportional to the number of edges is a
supercritical geometric Galton--Watson tree conditioned
to survive. The proof relies on enumeration results
obtained via the recent bijection given by the second
author together with Feray and Fusy.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Local limits, Unicellular maps, Lehmann-Walsh
formula",
}
@Article{Roberts:2013:IPR,
author = "Matthew Roberts and Lee Zhao",
title = "Increasing paths in regular trees",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "87:1--87:10",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2784",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2784",
abstract = "We consider a regular $n$-ary tree of height $h$, for
which every vertex except the root is labelled with an
independent and identically distributed continuous
random variable. Taking motivation from a question in
evolutionary biology, we consider the number of paths
from the root to a leaf along vertices with increasing
labels. We show that if $ \alpha = n / h$ is fixed and
$ \alpha > 1 / e$, the probability that there exists
such a path converges to $1$ as $ h \to \infty $. This
complements a previously known result that the
probability converges to $0$ if $ \alpha \leq 1 / e$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "branching processes; evolutionary biology; increasing
paths; trees",
}
@Article{Ding:2013:SMT,
author = "Jian Ding and Yuval Peres",
title = "Sensitivity of mixing times",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "88:1--88:6",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2765",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2765",
abstract = "In this note, we demonstrate an instance of
bounded-degree graphs of size $n$, for which the total
variation mixing time for the random walk is decreased
by a factor of $ \log n / \log \log n$ if we multiply
the edge-conductances by bounded factors in a certain
way.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "geometric bounds.; mixing time; sensitivity",
}
@Article{Baik:2013:AAP,
author = "Jinho Baik and Zhipeng Liu",
title = "On the average of the {Airy} process and its time
reversal",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "89:1--89:10",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2952",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2952",
abstract = "We show that the supremum of the average of the Airy
process and its time reversal minus a parabola is
distributed as the maximum of two independent GUE
Tracy-Widom random variables. The proof is obtained by
considering a directed last passage percolation model
with a rotational symmetry in two different ways. We
also review other known identities between the Airy
process and the Tracy-Widom distributions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
}
@Article{Wang:2013:WAF,
author = "Zhi Wang and Litan Yan and Xianye Yu",
title = "Weak approximation of the fractional {Brownian} sheet
from random walks",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "90:1--90:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2878",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2878",
abstract = "In this paper, we show an approximation in law of the
fractional Brownian sheet by random walks. As an
application, we consider a quasilinear stochastic heat
equation with Dirichlet boundary conditions driven by
an additive fractional noise.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Fractional Brownian sheet; random walks; stochastic
heat equation; weak convergence",
}
@Article{delBarrio:2013:BPS,
author = "Eustasio del Barrio and Arnold Janssen and Markus
Pauly",
title = "The $ m(n) $ out of $ k(n) $ bootstrap for partial
sums of {St. Petersburg} type games",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "91:1--91:10",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2772",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2772",
abstract = "This paper illustrates that the bootstrap of a partial
sum given by i.i.d. copies of a random variable $ X_1 $
has to be dealt with care in general. It turns out that
in various cases a whole spectrum of different limit
laws of the $ m(n) $ out of $ k(n) $ bootstrap can be
obtained for different choices of $ m(n) / k(n) - > 0 $
whenever $ X_1 $ does not lie in the domain of
attraction of a stable law. As a concrete example we
study bootstrap limit laws for the cumulated gain
sequence of repeated St. Petersburg games. It is shown
that here a continuum of different semi-stable
bootstrap limit laws occurs.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bootstrap, infinitely divisible distributions,
L\{\'e\}vy process, $m(n)$ out of $k(n)$ resampling,
stable and semi-stable laws, St. Petersburg game",
}
@Article{vandenBerg:2013:GBS,
author = "Jacob van den Berg and Rene Conijn",
title = "The gaps between the sizes of large clusters in 2D
critical percolation",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "92:1--92:9",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-3065",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/3065",
abstract = "Consider critical bond percolation on a large $ 2 n
\times 2 n $ box on the square lattice. It is
well-known that the size (i.e. number of vertices) of
the largest open cluster is, with high probability, of
order $ n^2 \pi (n) $, where $ \pi (n) $ denotes the
probability that there is an open path from the center
to the boundary of the box. The same result holds for
the second-largest cluster, the third largest cluster
et cetera.\par
J{\`a}rai showed that the differences between the sizes
of these clusters is, with high probability, at least
of order $ \sqrt {n^2 \pi (n)} $. Although this bound
was enough for his applications (to incipient infinite
clusters), he believed, but had no proof, that the
differences are in fact of the same order as the
cluster sizes themselves, i.e. $ n^2 \pi (n) $. Our
main result is a proof that this is indeed the case.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Critical percolation, cluster size",
}
@Article{Duminil-Copin:2013:LWC,
author = "Hugo Duminil-Copin",
title = "Limit of the {Wulff Crystal} when approaching
criticality for site percolation on the triangular
lattice",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "93:1--93:9",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-3163",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/3163",
abstract = "The understanding of site percolation on the
triangular lattice progressed greatly in the last
decade. Smirnov proved conformal invariance of critical
percolation, thus paving the way for the construction
of its scaling limit. Recently, the scaling limit of
near critical percolation was also constructed by
Garban, Pete and Schramm. The aim of this article is to
explain how these results imply the convergence, as $p$
tends to $ p_c$, of the Wulff crystal to a Euclidean
disk. The main ingredient of the proof is the
rotational invariance of the scaling limit of
near-critical percolation proved by these three
mathematicians.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "planar percolation, near-critical regime, surface
tension, Wulff crystal",
}
@Article{Masuda:2013:EEI,
author = "Hiroki Masuda and Nakahiro Yoshida",
title = "{Edgeworth} expansion for the integrated {L{\'e}vy}
driven {Ornstein--Uhlenbeck} process",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "94:1--94:10",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2726",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2726",
abstract = "We verify the Edgeworth expansion of any order for the
integrated ergodic L{\'e}vy driven Ornstein--Uhlenbeck
process, applying a Malliavin calculus with truncation
over the Wiener-Poisson space. Due to the special
structure of the model, each coefficient of the
expansion can be given in a closed form.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Edgeworth expansion; L{\'e}vy driven
Ornstein--Uhlenbeck process; mixing property",
}
@Article{Possamai:2013:RSM,
author = "Dylan Possama{\"\i} and Guillaume Royer and Nizar
Touzi",
title = "On the robust superhedging of measurable claims",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "95:1--95:13",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2739",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2739",
abstract = "The problem of robust hedging requires to solve the
problem of superhedging under a nondominated family of
singular measures. Recent progress was achieved by van
Handel, Neufeld, and Nutz. We show that the dual
formulation of this problem is valid in a context
suitable for martingale optimal transportation or, more
generally, for optimal transportation under controlled
stochastic dynamics.\par
",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "quasi-sure stochastic analysis.; Robust hedging",
}
@Article{Reitzner:2013:PPP,
author = "Matthias Reitzner",
title = "{Poisson} point processes: large deviation
inequalities for the convex distance",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "18",
pages = "96:1--96:7",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v18-2851",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2851",
abstract = "An analogue of Talagrand's convex distance for
binomial and Poisson point processes is defined. A
corresponding large deviation inequality is proved.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "convex distance; large deviation inequality; Poisson
point process",
}
@Article{Budhiraja:2014:UPT,
author = "Amarjit Budhiraja and Zhen-Qing Chen",
title = "On uniform positivity of transition densities of small
noise constrained diffusions",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "19",
pages = "1:1--1:9",
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v19-2967",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/2967",
abstract = "Constrained diffusions in convex polyhedral cones with
a general oblique reflection field, and with a
diffusion coefficient scaled by a small parameter $
\varepsilon > 0 $, are considered. Using an interior
Dirichlet heat kernel lower bound estimate for second
order elliptic operators in bounded domains from Zhang
(1995), certain uniform in $ \varepsilon $ lower bounds
on transition densities of such constrained diffusions
are established. These lower bounds together with
results from Biswas \& Budhiraja (2011) give, under
additional stability conditions, an exponential
leveling property as $ \varepsilon \to 0 $ for exit
times from suitable bounded domains.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Exponential leveling, reflected diffusions, Dirichlet
heat kernel estimates, Skorohod problem, exit time
estimates, Friedlin-Wentzell asymptotics.",
}
@Article{Zhu:2014:LDE,
author = "Lingjiong Zhu",
title = "On the large deviations for {Engel}'s, {Sylvester}'s
series and {Cantor}'s products",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "19",
pages = "2:1--2:9",
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v19-3194",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/3194",
abstract = "In this paper, we study the large deviations for
Engel's series, Sylvester's series and Cantor's
products from number theory.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Cantor's products; Engel's series; Large deviations;
Sylvester's series",
}
@Article{Guillotin-Plantard:2014:QFC,
author = "Nadine Guillotin-Plantard and Julien Poisat and Renato
Soares dos Santos",
title = "A quenched functional central limit theorem for planar
random walks in random sceneries",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "19",
pages = "3:1--3:9",
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v19-3002",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/3002",
abstract = "Random walks in random sceneries (RWRS) are simple
examples of stochastic processes in disordered media.
They were introduced at the end of the 70's by
Kesten-Spitzer and Borodin, motivated by the
construction of new self-similar processes with
stationary increments. Two sources of randomness enter
in their definition: a random field $ \xi = (\xi
(x))_{x \in \mathbb {Z}^d} $ of i.i.d. random
variables, which is called the random scenery, and a
random walk $ S = (S_n)_{n \in \mathbb {N}} $ evolving
in $ \mathbb {Z}^d $, independent of the scenery. The
RWRS $ Z = (Z_n)_{n \in \mathbb {N}} $ is then defined
as the accumulated scenery along the trajectory of the
random walk, i.e., $ Z_n := \sum_{k = 1}^n \xi (S_k) $.
The law of $Z$ under the joint law of $ \xi $ and $S$
is called {"annealed}'', and the conditional law given
$ \xi $ is called {"quenched}''. Recently, functional
central limit theorems under the quenched law were
proved for $Z$ by the first two authors for a class of
transient random walks including walks with finite
variance in dimension $ d \ge 3$. In this paper we
extend their results to dimension $ d = 2$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Associated Random Variables; Limit theorem; Local
time; Random walk in random scenery",
}
@Article{Benaych-Georges:2014:LEE,
author = "Florent Benaych-Georges and Sandrine P{\'e}ch{\'e}",
title = "Largest eigenvalues and eigenvectors of band or sparse
random matrices",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "19",
pages = "4:1--4:9",
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v19-3027",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/3027",
abstract = "In this text, we consider an $N$ by $N$ random matrix
$X$ such that all but $ o(N)$ rows of $X$ have $W$ non
identically zero entries, the other rows having less
than $W$ entries (such as, for example, standard or
cyclic band matrices). We always suppose that $ 1 \ll W
\ll N$. We first prove that if the entries are
independent, centered, have variance one, satisfy a
certain tail upper-bound condition and $ W \gg (\log
N)^{6(1 + \alpha)}$, where $ \alpha $ is a positive
parameter depending on the distribution of the entries,
then the largest eigenvalue of $ X / \sqrt {W}$
converges to the upper bound of its limit spectral
distribution, that is $2$, as for Wigner matrices. This
extends some previous results by Khorunzhiy and Sodin
where less hypotheses were made on $W$, but more
hypotheses were made about the law of the entries and
the structure of the matrix. Then, under the same
hypotheses, we prove a delocalization result for the
eigenvectors of $X$, precisely that most of them cannot
be essentially localized on less than $ W / \log (N)$
entries. This lower bound on the localization length
has to be compared to the recent result by
Steinerberger, which states that the localization
length in the edge is $ \ll W^{7 / 5}$ or there is
strong interaction between two eigenvectors in an
interval of length $ W^{7 / 5}$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "band matrices; largest eigenvalues; localization;
random matrices",
}
@Article{Hamana:2014:APD,
author = "Yuji Hamana and Hiroyuki Matsumoto",
title = "Asymptotics of the probability distributions of the
first hitting times of {Bessel} processes",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "19",
pages = "5:1--5:5",
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v19-3215",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/3215",
abstract = "The asymptotic behavior of the tail probabilities for
the first hitting times of the Bessel process with
arbitrary index is shown without using the explicit
expressions for the distribution function obtained in
the authors' previous works.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Bessel process; hitting time; tail probability",
}
@Article{Devroye:2014:PNF,
author = "Luc Devroye and Svante Janson",
title = "Protected nodes and fringe subtrees in some random
trees",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "19",
pages = "6:1--6:10",
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v19-3048",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/3048",
abstract = "We study protected nodes in various classes of random
rooted trees by putting them in the general context of
fringe subtrees introduced by Aldous (1991). Several
types of random trees are considered: simply generated
trees (or conditioned Galton--Watson trees), which
includes several cases treated separately by other
authors, binary search trees and random recursive
trees. This gives unified and simple proofs of several
earlier results, as well as new results.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "binary search trees; conditioned Galton--Watson trees;
fringe trees; protected nodes; random recursive trees;
simply generated trees",
}
@Article{Wojtylak:2014:SPC,
author = "Micha{\l} Wojtylak and Patryk Pagacz",
title = "On the spectral properties of a class of
{$H$}-selfadjoint random matrices and the underlying
combinatorics",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "19",
pages = "7:1--7:14",
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v19-3066",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/3066",
abstract = "An expansion of the Weyl function of a $H$-selfadjoint
random matrix with one negative square is provided. It
is shown that the coefficients converge to a certain
generalization of Catlan numbers. Properties of this
generalization are studied, in particular, a
combinatorial interpretation is given.",
acknowledgement = ack-nhfb,
ajournal = "Electron. Commun. Probab.",
fjournal = "Electronic Communications in Probability",
journal-URL = "http://ecp.ejpecp.org/",
keywords = "Catalan numbers; eigenvalue of nonpositive type;
H-selfadjoint matrix; Wigner matrix",
}
@Article{Marchand:2014:RBP,
author = "{\'E}ric Marchand and Djilali Ait Aoudia and
Fran{\c{c}}ois Perron and Latifa Ben Hadj Slimene",
title = "On runs, bivariate {Poisson} mixtures and
distributions that arise in {Bernoulli} arrays",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "19",
pages = "8:1--8:12",
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1214/ECP.v19-3152",
ISSN = "1083-589X",
ISSN-L = "1083-589X",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ecp.bib",
URL = "http://ecp.ejpecp.org/article/view/3152",
abstract = "Distributional findings are obtained relative to
various quantities arising in Bernoulli arrays $ \{
X_{k, j}, k \geq 1, j = 1, \ldots, r + 1 \} $, where
the rows $ (X_{k, 1}, \ldots, X_{k, r + 1}) $ are
independently distributed as $ \hbox {Multinomial}(1,
p_{k, 1}, \ldots,