@Preamble{
"\ifx \undefined \cprime \def \cprime {$'$}\fi" #
"\ifx \undefined \flqq \def \flqq {\ifmmode \ll \else \leavevmode \raise 0.2ex \hbox{$\scriptscriptstyle \ll $}\fi}\fi" #
"\ifx \undefined \frqq \def \frqq {\ifmmode \gg \else \leavevmode \raise 0.2ex \hbox{$\scriptscriptstyle \gg $}\fi}\fi" #
"\ifx \undefined \k \let \k = \c \fi" #
"\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}}\fi" #
"\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi" #
"\ifx \undefined \mathfrak \let \mathfrak = \mathcal \fi" #
"\ifx \undefined \mathscr \def \mathscr #1{{\cal #1}}\fi" #
"\ifx \undefined \text \def \text #1{{\hbox{\rm #1}}}\fi"
}
@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/|"}
@String{j-ELECTRON-J-PROBAB = "Electronic Journal of Probability"}
@Article{Khoshnevisan:1996:LCS,
author = "Davar Khoshnevisan",
title = "{L{\'e}vy} classes and self-normalization",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "1:1--1:18",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-1",
ISSN = "1083-6489",
MRclass = "60F15 (60J15 60J45 60J55)",
MRnumber = "1386293 (97h:60024)",
MRreviewer = "Qi Man Shao",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/1;
http://www.math.washington.edu/~ejpecp/EjpVol1/paper1.abs.html",
abstract = "We prove a Chung's law of the iterated logarithm for
recurrent linear Markov processes. In order to attain
this level of generality, our normalization is random.
In particular, when the Markov process in question is a
diffusion, we obtain the integral test corresponding to
a law of the iterated logarithm due to Knight.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Self-normalization, Levy Classes",
}
@Article{Lawler:1996:HDC,
author = "Gregory F. Lawler",
title = "{Hausdorff} dimension of cut points for {Brownian}
motion",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "2:1--2:20",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-2",
ISSN = "1083-6489",
MRclass = "60J65",
MRnumber = "1386294 (97g:60111)",
MRreviewer = "Paul McGill",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/2",
abstract = "Let $B$ be a Brownian motion in $ R^d$, $ d = 2, 3$. A
time $ t \in [0, 1]$ is called a cut time for $ B[0,
1]$ if $ B[0, t) \cap B(t, 1] = \emptyset $. We show
that the Hausdorff dimension of the set of cut times
equals $ 1 - \zeta $, where $ \zeta = \zeta_d$ is the
intersection exponent. The theorem, combined with known
estimates on $ \zeta_3$, shows that the percolation
dimension of Brownian motion (the minimal Hausdorff
dimension of a subpath of a Brownian path) is strictly
greater than one in $ R^3$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion, Hausdorff dimension, cut points,
intersection exponent",
}
@Article{Bass:1996:EEB,
author = "Richard F. Bass and Krzysztof Burdzy",
title = "Eigenvalue expansions for {Brownian} motion with an
application to occupation times",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "3:1--3:19",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-3",
ISSN = "1083-6489",
MRclass = "60J65",
MRnumber = "1386295 (97c:60201)",
MRreviewer = "Zhong Xin Zhao",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/3;
http://www.math.washington.edu/~ejpecp/EjpVol1/paper3.abs.html",
abstract = "Let $B$ be a Borel subset of $ R^d$ with finite
volume. We give an eigenvalue expansion for the
transition densities of Brownian motion killed on
exiting $B$. Let $ A_1$ be the time spent by Brownian
motion in a closed cone with vertex $0$ until time one.
We show that $ \lim_{u \to 0} \log P^0 (A_1 < u) / \log
u = 1 / \xi $ where $ \xi $ is defined in terms of the
first eigenvalue of the Laplacian in a compact domain.
Eigenvalues of the Laplacian in open and closed sets
are compared.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion, eigenfunction expansion, eigenvalues,
arcsine law",
}
@Article{Pitman:1996:RDD,
author = "Jim Pitman and Marc Yor",
title = "Random Discrete Distributions Derived from
Self-Similar Random Sets",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "4:1--4:28",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-4",
ISSN = "1083-6489",
MRclass = "60D05",
MRnumber = "1386296 (98i:60010)",
MRreviewer = "Bert Fristedt",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/4",
abstract = "A model is proposed for a decreasing sequence of
random variables $ (V_1, V_2, \cdots) $ with $ \sum_n
V_n = 1 $, which generalizes the Poisson--Dirichlet
distribution and the distribution of ranked lengths of
excursions of a Brownian motion or recurrent Bessel
process. Let $ V_n $ be the length of the $n$ th
longest component interval of $ [0, 1] \backslash Z$,
where $Z$ is an a.s. non-empty random closed of $ (0,
\infty)$ of Lebesgue measure $0$, and $Z$ is
self-similar, i.e., $ c Z$ has the same distribution as
$Z$ for every $ c > 0$. Then for $ 0 \leq a < b \leq 1$
the expected number of $n$'s such that $ V_n \in (a,
b)$ equals $ \int_a^b v^{-1} F(d v)$ where the
structural distribution $F$ is identical to the
distribution of $ 1 - \sup (Z \cap [0, 1])$. Then $ F(d
v) = f(v)d v$ where $ (1 - v) f(v)$ is a decreasing
function of $v$, and every such probability
distribution $F$ on $ [0, 1]$ can arise from this
construction.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "interval partition, zero set, excursion lengths,
regenerative set, structural distribution",
}
@Article{Seppalainen:1996:MMB,
author = "Timo Sepp{\"a}l{\"a}inen",
title = "A microscopic model for the {Burgers} equation and
longest increasing subsequences",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "5:1--5:51",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-5",
ISSN = "1083-6489",
MRclass = "60K35 (35Q53 60C05 82C22)",
MRnumber = "1386297 (97d:60162)",
MRreviewer = "Shui Feng",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/5",
abstract = "We introduce an interacting random process related to
Ulam's problem, or finding the limit of the normalized
longest increasing subsequence of a random permutation.
The process describes the evolution of a configuration
of sticks on the sites of the one-dimensional integer
lattice. Our main result is a hydrodynamic scaling
limit: The empirical stick profile converges to a weak
solution of the inviscid Burgers equation under a
scaling of lattice space and time. The stick process is
also an alternative view of Hammersley's particle
system that Aldous and Diaconis used to give a new
solution to Ulam's problem. Along the way to the
scaling limit we produce another independent solution
to this question. The heart of the proof is that
individual paths of the stochastic process evolve under
a semigroup action which under the scaling turns into
the corresponding action for the Burgers equation,
known as the Lax formula. In a separate appendix we use
the Lax formula to give an existence and uniqueness
proof for scalar conservation laws with initial data
given by a Radon measure.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Hydrodynamic scaling limit, Ulam's problem,
Hammersley's process, nonlinear conservation law, the
Burgers equation, the Lax formula",
}
@Article{Fleischmann:1996:TSA,
author = "Klaus Fleischmann and Andreas Greven",
title = "Time-Space Analysis of the Cluster-Formation in
Interacting Diffusions",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "6:1--6:46",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-6",
ISSN = "1083-6489",
MRclass = "60K35 (60J60)",
MRnumber = "1386298 (97e:60151)",
MRreviewer = "Ingemar Kaj",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/6",
abstract = "A countable system of linearly interacting diffusions
on the interval [0, 1], indexed by a hierarchical group
is investigated. A particular choice of the
interactions guarantees that we are in the diffusive
clustering regime, that is spatial clusters of
components with values all close to 0 or all close to 1
grow in various different scales. We studied this
phenomenon in [FG94]. In the present paper we analyze
the evolution of single components and of clusters over
time. First we focus on the time picture of a single
component and find that components close to 0 or close
to 1 at a late time have had this property for a large
time of random order of magnitude, which nevertheless
is small compared with the age of the system. The
asymptotic distribution of the suitably scaled duration
a component was close to a boundary point is
calculated. Second we study the history of spatial 0-
or 1-clusters by means of time scaled block averages
and time-space-thinning procedures. The scaled age of a
cluster is again of a random order of magnitude. Third,
we construct a transformed Fisher--Wright tree, which
(in the long-time limit) describes the structure of the
space-time process associated with our system. All
described phenomena are independent of the diffusion
coefficient and occur for a large class of initial
configurations (universality).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "interacting diffusion, clustering, infinite particle
system, delayed coalescing random walk with
immigration, transformed Fisher--Wright tree, low
dimensional systems, ensemble of log-coalescents",
}
@Article{Bryc:1996:CMR,
author = "W{\l}odzimierz Bryc",
title = "Conditional Moment Representations for Dependent
Random Variables",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "7:1--7:14",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-7",
ISSN = "1083-6489",
MRclass = "60A10 (60B99 60E15 62J12)",
MRnumber = "1386299 (97j:60004)",
MRreviewer = "M. M. Rao",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/7",
abstract = "The question considered in this paper is which
sequences of $p$-integrable random variables can be
represented as conditional expectations of a fixed
random variable with respect to a given sequence of
sigma-fields. For finite families of sigma-fields,
explicit inequality equivalent to solvability is
stated; sufficient conditions are given for finite and
infinite families of sigma-fields, and explicit
expansions are presented.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "alternating conditional expectation, inverse problems,
ACE",
}
@Article{Liao:1996:ASE,
author = "Xiao Xin Liao and Xuerong Mao",
title = "Almost Sure Exponential Stability of Neutral
Differential Difference Equations with Damped
Stochastic Perturbations",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "8:1--8:16",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-8",
ISSN = "1083-6489",
MRclass = "60H10 (34K40)",
MRnumber = "1386300 (97d:60100)",
MRreviewer = "Tom{\'a}s Caraballo",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/8",
abstract = "In this paper we shall discuss the almost sure
exponential stability for a neutral differential
difference equation with damped stochastic
perturbations of the form $ d[x(t) - G(x(t - \tau))] =
f(t, x(t), x(t - \tau))d t + \sigma (t) d w(t) $.
Several interesting examples are also given for
illustration. It should be pointed out that our results
are even new in the case when $ \sigma (t) \equiv 0 $,
i.e., for deterministic neutral differential difference
equations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "neutral equations, stochastic perturbation,
exponential martingale inequality, Borel--Cantelli's
lemma, Lyapunov exponent",
}
@Article{Roberts:1996:QBC,
author = "Gareth O. Roberts and Jeffrey S. Rosenthal",
title = "Quantitative bounds for convergence rates of
continuous time {Markov} processes",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "9:1--9:21",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-9",
ISSN = "1083-6489",
MRclass = "60J25",
MRnumber = "1423462 (97k:60198)",
MRreviewer = "Mu Fa Chen",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/9",
abstract = "We develop quantitative bounds on rates of convergence
for continuous-time Markov processes on general state
spaces. Our methods involve coupling and
shift-coupling, and make use of minorization and drift
conditions. In particular, we use auxiliary coupling to
establish the existence of small (or pseudo-small)
sets. We apply our method to some diffusion examples.
We are motivated by interest in the use of Langevin
diffusions for Monte Carlo simulation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Markov process, rates of convergence, coupling,
shift-coupling, minorization condition, drift
condition",
}
@Article{Arous:1996:MTD,
author = "G{\'e}rard Ben Arous and Rapha{\"e}l Cerf",
title = "Metastability of the Three Dimensional {Ising} Model
on a Torus at Very Low Temperatures",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "10:1--10:55",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-10",
ISSN = "1083-6489",
MRclass = "82C44 (05B50 60J10 60K35)",
MRnumber = "1423463 (98a:82086)",
MRreviewer = "Peter Eichelsbacher",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/10;
http://www.math.washington.edu/~ejpecp/EjpVol1/paper10.abs.html",
abstract = "We study the metastability of the stochastic three
dimensional Ising model on a finite torus under a small
positive magnetic field at very low temperatures.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Ising, metastability, droplet, Freidlin--Wentzell
theory, large deviations",
}
@Article{Bass:1996:USE,
author = "Richard F. Bass",
title = "Uniqueness for the {Skorokhod} equation with normal
reflection in {Lipschitz} domains",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "11:1--11:29",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-11",
ISSN = "1083-6489",
MRclass = "60J60 (60J50)",
MRnumber = "1423464 (98d:60155)",
MRreviewer = "Zhen-Qing Chen",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/11;
http://www.math.washington.edu/~ejpecp/EjpVol1/paper11.abs.html",
abstract = "We consider the Skorokhod equation\par
$$ d X_t = d W_t + (1 / 2) \nu (X_t), d L_t $$
in a domain $D$, where $ W_t$ is Brownian motion in $
R^d$, $ \nu $ is the inward pointing normal vector on
the boundary of $D$, and $ L_t$ is the local time on
the boundary. The solution to this equation is
reflecting Brownian motion in $D$. In this paper we
show that in Lipschitz domains the solution to the
Skorokhod equation is unique in law.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Lipschitz domains, Neumann problem, reflecting
Brownian motion, mixed boundary problem, Skorokhod
equation, weak uniqueness, uniqueness in law,
submartingale problem",
}
@Article{Gravner:1996:PTT,
author = "Janko Gravner",
title = "Percolation Times in Two-Dimensional Models For
Excitable Media",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "12:1--12:19",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-12",
ISSN = "1083-6489",
MRclass = "60K35 (90C27)",
MRnumber = "1423465 (98c:60141)",
MRreviewer = "Rahul Roy",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/12",
abstract = "The three-color {\em Greenberg--Hastings model (GHM) }
is a simple cellular automaton model for an excitable
medium. Each site on the lattice $ Z^2 $ is initially
assigned one of the states 0, 1 or 2. At each tick of a
discrete--time clock, the configuration changes
according to the following synchronous rule: changes $
1 \to 2 $ and $ 2 \to 0 $ are automatic, while an $x$
in state 0 may either stay in the same state or change
to 1, the latter possibility occurring iff there is at
least one representative of state 1 in the local
neighborhood of $x$. Starting from a product measure
with just 1's and 0's such dynamics quickly die out
(turn into 0's), but not before 1's manage to form
infinite connected sets. A very precise description of
this ``transient percolation'' phenomenon can be
obtained when the neighborhood of $x$ consists of 8
nearest points, the case first investigated by S.
Fraser and R. Kapral. In addition, first percolation
times for related monotone models are addressed.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "additive growth dynamics, excitable media,
Greenberg--Hastings model, percolation",
}
@Article{Lawler:1996:CTS,
author = "Gregory F. Lawler",
title = "Cut Times for Simple Random Walk",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "13:1--13:24",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-13",
ISSN = "1083-6489",
MRclass = "60J15 (60J65)",
MRnumber = "1423466 (97i:60088)",
MRreviewer = "Thomas Polaski",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/13",
abstract = "Let $ S(n) $ be a simple random walk taking values in
$ Z^d $. A time $n$ is called a cut time if \par
$$ S[0, n] \cap S[n + 1, \infty) = \emptyset . $$
We show that in three dimensions the number of cut
times less than $n$ grows like $ n^{1 - \zeta }$ where
$ \zeta = \zeta_d$ is the intersection exponent. As
part of the proof we show that in two or three
dimensions \par
$$ P(S[0, n] \cap S[n + 1, 2 n] = \emptyset) \sim n^{-
\zeta }, $$
where $ \sim $ denotes that each side is bounded by a
constant times the other side.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Random walk, cut points, intersection exponent",
}
@Article{Dawson:1996:MST,
author = "Donald A. Dawson and Andreas Greven",
title = "Multiple Space-Time Scale Analysis For Interacting
Branching Models",
journal = j-ELECTRON-J-PROBAB,
volume = "1",
pages = "14:1--14:84",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v1-14",
ISSN = "1083-6489",
MRclass = "60K35 (60J80)",
MRnumber = "1423467 (97m:60148)",
MRreviewer = "Jean Vaillancourt",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/14",
abstract = "We study a class of systems of countably many linearly
interacting diffusions whose components take values in
$ [0, \inf) $ and which in particular includes the case
of interacting (via migration) systems of Feller's
continuous state branching diffusions. The components
are labelled by a hierarchical group. The longterm
behaviour of this system is analysed by considering
space-time renormalised systems in a combination of
slow and fast time scales and in the limit as an
interaction parameter goes to infinity. This leads to a
new perspective on the large scale behaviour (in space
and time) of critical branching systems in both the
persistent and non-persistent cases and including that
of the associated historical process. Furthermore we
obtain an example for a rigorous renormalization
analysis.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Branching processes, interacting diffusions, super
random walk, renormalization, historical processes",
}
@Article{Takacs:1997:RWP,
author = "Christiane Takacs",
title = "Random Walk on Periodic Trees",
journal = j-ELECTRON-J-PROBAB,
volume = "2",
pages = "1:1--1:16",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v2-15",
ISSN = "1083-6489",
MRclass = "60J15",
MRnumber = "1436761 (97m:60101)",
MRreviewer = "Jochen Geiger",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/15",
abstract = "Following Lyons (1990, Random Walks and Percolation on
Trees) we define a periodic tree, restate its branching
number and consider a biased random walk on it. In the
case of a transient walk, we describe the
walk-invariant random periodic tree and calculate the
asymptotic rate of escape (speed) of the walk. This is
achieved by exploiting the connections between random
walks and electric networks.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Trees, Random Walk, Speed",
}
@Article{Rosen:1997:LIL,
author = "Jay Rosen",
title = "Laws of the Iterated Logarithm for Triple
Intersections of Three Dimensional Random Walks",
journal = j-ELECTRON-J-PROBAB,
volume = "2",
pages = "2:1--2:32",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v2-16",
ISSN = "1083-6489",
MRclass = "60F15 (60J15)",
MRnumber = "1444245 (98d:60063)",
MRreviewer = "Karl Grill",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/16",
abstract = "Let $ X = X_n, X' = X'_n $, and $ X'' = X''_n $, $ n
\geq 1 $, be three independent copies of a symmetric
three dimensional random walk with $ E(|X_1 |^2 \log_+
|X_1 |) $ finite. In this paper we study the
asymptotics of $ I_n $, the number of triple
intersections up to step $n$ of the paths of $ X, X'$
and $ X''$ as $n$ goes to infinity. Our main result
says that the limsup of $ I_n$ divided by $ \log (n)
\log_3 (n)$ is equal to $ 1 \over \pi |Q|$, a.s., where
$Q$ denotes the covariance matrix of $ X_1$. A similar
result holds for $ J_n$, the number of points in the
triple intersection of the ranges of $ X, X'$ and $
X''$ up to step $n$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "random walks, intersections",
}
@Article{Abraham:1997:APB,
author = "Romain Abraham and Wendelin Werner",
title = "Avoiding-probabilities for {Brownian} snakes and
super-{Brownian} motion",
journal = j-ELECTRON-J-PROBAB,
volume = "2",
pages = "3:1--3:27",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v2-17",
ISSN = "1083-6489",
MRclass = "60J25 (60G57)",
MRnumber = "1447333 (98j:60100)",
MRreviewer = "John Verzani",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/17",
abstract = "We investigate the asymptotic behaviour of the
probability that a normalized $d$-dimensional Brownian
snake (for instance when the life-time process is an
excursion of height 1) avoids 0 when starting at
distance $ \varepsilon $ from the origin. In particular
we show that when $ \varepsilon $ tends to 0, this
probability respectively behaves (up to multiplicative
constants) like $ \varepsilon^4$, $ \varepsilon^{2
\sqrt {2}}$ and $ \varepsilon^{(\sqrt {17} - 1) / 2}$,
when $ d = 1$, $ d = 2$ and $ d = 3$. Analogous results
are derived for super-Brownian motion started from $
\delta_x$ (conditioned to survive until some time) when
the modulus of $x$ tends to 0.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian snakes, superprocesses, non-linear
differential equations",
}
@Article{Jakubowski:1997:NST,
author = "Adam Jakubowski",
title = "A non-{Skorohod} topology on the {Skorohod} space",
journal = j-ELECTRON-J-PROBAB,
volume = "2",
pages = "4:1--4:21",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v2-18",
ISSN = "1083-6489",
MRclass = "60F17 (60B05 60B10 60G17)",
MRnumber = "1475862 (98k:60046)",
MRreviewer = "Ireneusz Szyszkowski",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/18",
abstract = "A new topology (called $S$) is defined on the space
$D$ of functions $ x \colon [0, 1] \to R^1$ which are
right-continuous and admit limits from the left at each
$ t > 0$. Although $S$ cannot be metricized, it is
quite natural and shares many useful properties with
the traditional Skorohod's topologies $ J_1$ and $
M_1$. In particular, on the space $ P(D)$ of laws of
stochastic processes with trajectories in $D$ the
topology $S$ induces a sequential topology for which
both the direct and the converse Prokhorov's theorems
are valid, the a.s. Skorohod representation for
subsequences exists and finite dimensional convergence
outside a countable set holds.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Skorohod space, Skorohod representation, convergence
in distribution, sequential spaces, semimartingales",
}
@Article{Arcones:1997:LIL,
author = "Miguel A. Arcones",
title = "The Law of the Iterated Logarithm for a Triangular
Array of Empirical Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "2",
pages = "5:1--5:39",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v2-19",
ISSN = "1083-6489",
MRclass = "60B12 (60F15)",
MRnumber = "1475863 (98k:60006)",
MRreviewer = "Winfried Stute",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/19",
abstract = "We study the compact law of the iterated logarithm for
a certain type of triangular arrays of empirical
processes, appearing in statistics (M-estimators,
regression, density estimation, etc). We give necessary
and sufficient conditions for the law of the iterated
logarithm of these processes of the type of conditions
used in Ledoux and Talagrand (1991): convergence in
probability, tail conditions and total boundedness of
the parameter space with respect to certain
pseudometric. As an application, we consider the law of
the iterated logarithm for a class of density
estimators. We obtain the order of the optimal window
for the law of the iterated logarithm of density
estimators. We also consider the compact law of the
iterated logarithm for kernel density estimators when
they have large deviations similar to those of a
Poisson process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Empirical process, law of the iterated logarithm,
triangular array, density estimation",
}
@Article{Bertoin:1997:CPV,
author = "Jean Bertoin",
title = "{Cauchy}'s Principal Value of Local Times of
{L{\'e}vy} Processes with no Negative Jumps via
Continuous Branching Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "2",
pages = "6:1--6:12",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v2-20",
ISSN = "1083-6489",
MRclass = "60J30 (60J55)",
MRnumber = "1475864 (99b:60120)",
MRreviewer = "N. H. Bingham",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/20",
abstract = "Let $X$ be a recurrent L{\'e}vy process with no
negative jumps and $n$ the measure of its excursions
away from $0$. Using Lamperti's connection that links
$X$ to a continuous state branching process, we
determine the joint distribution under $n$ of the
variables $ C^+_T = \int_0^T{\bf 1}_{{X_s >
0}}X_s^{-1}d s$ and $ C^-_T = \int_0^T{\bf 1}_{{X_s <
0}}|X_s|^{-1}d s$, where $T$ denotes the duration of
the excursion. This provides a new insight on an
identity of Fitzsimmons and Getoor on the Hilbert
transform of the local times of $X$. Further results in
the same vein are also discussed.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Cauchy's principal value, L{\'e}vy process with no
negative jumps, branching process",
}
@Article{Mueller:1997:FWR,
author = "Carl Mueller and Roger Tribe",
title = "Finite Width For a Random Stationary Interface",
journal = j-ELECTRON-J-PROBAB,
volume = "2",
pages = "7:1--7:27",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v2-21",
ISSN = "1083-6489",
MRclass = "60H15 (35R60)",
MRnumber = "1485116 (99g:60106)",
MRreviewer = "Richard B. Sowers",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/21",
abstract = "We study the asymptotic shape of the solution $ u(t,
x) \in [0, 1] $ to a one-dimensional heat equation with
a multiplicative white noise term. At time zero the
solution is an interface, that is $ u(0, x) $ is 0 for
all large positive $x$ and $ u(0, x)$ is 1 for all
large negative $x$. The special form of the noise term
preserves this property at all times $ t \geq 0$. The
main result is that, in contrast to the deterministic
heat equation, the width of the interface remains
stochastically bounded.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic partial differential equations, duality,
travelling waves, white noise",
}
@Article{Kager:1997:GOS,
author = "Gerald Kager and Michael Scheutzow",
title = "Generation of One-Sided Random Dynamical Systems by
Stochastic Differential Equations",
journal = j-ELECTRON-J-PROBAB,
volume = "2",
pages = "8:1--8:17",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v2-22",
ISSN = "1083-6489",
MRclass = "60H10 (28D10 34C35 34F05)",
MRnumber = "1485117 (99b:60080)",
MRreviewer = "Xue Rong Mao",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/22",
abstract = "Let $Z$ be an $ R^m$-valued semimartingale with
stationary increments which is realized as a helix over
a filtered metric dynamical system $S$. Consider a
stochastic differential equation with Lipschitz
coefficients which is driven by $Z$. We show that its
solution semiflow $ \phi $ has a version for which $
\varphi (t, \omega) = \phi (0, t, \omega)$ is a cocycle
and therefore ($S$, $ \varphi $) is a random dynamical
system. Our results generalize previous results which
required $Z$ to be continuous. We also address the case
of local Lipschitz coefficients with possible blow-up
in finite time. Our abstract perfection theorems are
designed to cover also potential applications to
infinite dimensional equations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "stochastic differential equation, random dynamical
system, cocycle, perfection",
}
@Article{Chaleyat-Maurel:1997:PPD,
author = "Mireille Chaleyat-Maurel and David Nualart",
title = "Points of Positive Density for Smooth Functionals",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "1:1--1:8",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-23",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/23",
abstract = "In this paper we show that the set of points where the
density of a Wiener functional is strictly positive is
an open connected set, assuming some regularity
conditions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Nondegenerate smooth Wiener functionals, Malliavin
calculus, Support of the law",
}
@Article{Chaleyat-Maurel:1998:PPD,
author = "Mireille Chaleyat-Maurel and David Nualart",
title = "Points of positive density for smooth functionals",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "1:1--1:8",
year = "1998",
CODEN = "????",
ISSN = "1083-6489",
MRclass = "60H07",
MRnumber = "1487202 (99b:60072)",
MRreviewer = "Shi Zan Fang",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://www.math.washington.edu/~ejpecp/EjpVol3/paper1.abs.html",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Hitczenko:1998:HCM,
author = "Pawe{\l} Hitczenko and Stanis{\l}aw Kwapie{\'n} and
Wenbo V. Li and Gideon Schechtman and Thomas
Schlumprecht and Joel Zinn",
title = "Hypercontractivity and Comparison of Moments of
Iterated Maxima and Minima of Independent Random
Variables",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "2:1--2:26",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-24",
ISSN = "1083-6489",
MRclass = "60B11 (52A21 60E07 60E15 60G15)",
MRnumber = "1491527 (99k:60008)",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/24",
abstract = "We provide necessary and sufficient conditions for
hypercontractivity of the minima of nonnegative, i.i.d.
random variables and of both the maxima of minima and
the minima of maxima for such r.v.'s. It turns out that
the idea of hypercontractivity for minima is closely
related to small ball probabilities and Gaussian
correlation inequalities.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "hypercontractivity, comparison of moments, iterated
maxima and minima, Gaussian correlation inequalities,
small ball probabilities",
}
@Article{Aldous:1998:EBM,
author = "David Aldous and Vlada Limic",
title = "The Entrance Boundary of the Multiplicative
Coalescent",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "3:1--3:59",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-25",
ISSN = "1083-6489",
MRclass = "60J50 (60J75)",
MRnumber = "1491528 (99d:60086)",
MRreviewer = "M. G. Shur",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/25",
abstract = "The multiplicative coalescent $ X(t) $ is a $
l^2$-valued Markov process representing coalescence of
clusters of mass, where each pair of clusters merges at
rate proportional to product of masses. From random
graph asymptotics it is known (Aldous (1997)) that
there exists a {\em standard} version of this process
starting with infinitesimally small clusters at time $
- \infty $. In this paper, stochastic calculus
techniques are used to describe all versions $ (X(t); -
\infty < t < \infty)$ of the multiplicative coalescent.
Roughly, an extreme version is specified by translation
and scale parameters, and a vector $ c \in l^3$ of
relative sizes of large clusters at time $ - \infty $.
Such a version may be characterized in three ways: via
its $ t \to - \infty $ behavior, via a representation
of the marginal distribution $ X(t)$ in terms of
excursion-lengths of a L{\'e}vy-type process, or via a
weak limit of processes derived from the standard
version via a ``coloring'' construction.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Markov process, entrance boundary, excursion, L{\'e}vy
process, random graph, stochastic coalescent, weak
convergence",
}
@Article{Cranston:1998:GEU,
author = "Michael Cranston and Yves {Le Jan}",
title = "Geometric Evolution Under Isotropic Stochastic Flow",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "4:1--4:36",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-26",
ISSN = "1083-6489",
MRclass = "60H10 (60J60)",
MRnumber = "1610230 (99c:60115)",
MRreviewer = "R{\'e}mi L{\'e}andre",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/26",
abstract = "Consider an embedded hypersurface $M$ in $ R^3$. For $
\Phi_t$ a stochastic flow of differomorphisms on $ R^3$
and $ x \in M$, set $ x_t = \Phi_t (x)$ and $ M_t =
\Phi_t (M)$. In this paper we will assume $ \Phi_t$ is
an isotropic (to be defined below) measure preserving
flow and give an explicit description by SDE's of the
evolution of the Gauss and mean curvatures, of $ M_t$
at $ x_t$. If $ \lambda_1 (t)$ and $ \lambda_2 (t)$ are
the principal curvatures of $ M_t$ at $ x_t$ then the
vector of mean curvature and Gauss curvature, $
(\lambda_1 (t) + \lambda_2 (t)$, $ \lambda_1 (t)
\lambda_2 (t))$, is a recurrent diffusion. Neither
curvature by itself is a diffusion. In a separate
addendum we treat the case of $M$ an embedded
codimension one submanifold of $ R^n$. In this case,
there are $ n - 1$ principal curvatures $ \lambda_1
(t), \ldots {}, \lambda_{n - 1} (t)$. If $ P_k, k = 1,
\dots, n - 1$ are the elementary symmetric polynomials
in $ \lambda_1, \ldots {}, \lambda_{n - 1}$, then the
vector $ (P_1 (\lambda_1 (t), \ldots {}, \lambda_{n -
1} (t)), \ldots {}, P_{n - 1} (\lambda_1 (t), \ldots
{}, \lambda_{n - 1} (t))$ is a diffusion and we compute
the generator explicitly. Again no projection of this
diffusion onto lower dimensions is a diffusion. Our
geometric study of isotropic stochastic flows is a
natural offshoot of earlier works by Baxendale and
Harris (1986), LeJan (1985, 1991) and Harris (1981).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic flows, Lyapunov exponents, principal
curvatures",
}
@Article{Evans:1998:CLT,
author = "Steven N. Evans and Edwin A. Perkins",
title = "Collision Local Times, Historical Stochastic Calculus,
and Competing Species",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "5:1--5:120",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-27",
ISSN = "1083-6489",
MRclass = "60G57 (60H99 60J55 60J80)",
MRnumber = "1615329 (99h:60098)",
MRreviewer = "Anton Wakolbinger",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/27",
abstract = "Branching measure-valued diffusion models are
investigated that can be regarded as pairs of
historical Brownian motions modified by a competitive
interaction mechanism under which individuals from each
population have their longevity or fertility adversely
affected by collisions with individuals from the other
population. For 3 or fewer spatial dimensions, such
processes are constructed using a new fixed-point
technique as the unique solution of a strong equation
driven by another pair of more explicitly constructible
measure-valued diffusions. This existence and
uniqueness is used to establish well-posedness of the
related martingale problem and hence the strong Markov
property for solutions. Previous work of the authors
has shown that in 4 or more dimensions models with the
analogous definition do not exist.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "super-process, super-Brownian motion, interaction,
local time, historical process, measure-valued Markov
branching process, stochastic calculus, martingale
measure, random measure",
xxtitle = "Collision local times, historical stochastic calculus,
and competing superprocesses",
}
@Article{Ferrari:1998:FSS,
author = "P. A. Ferrari and L. R. G. Fontes",
title = "Fluctuations of a Surface Submitted to a Random
Average Process",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "6:1--6:34",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-28",
ISSN = "1083-6489",
MRclass = "60K35",
MRnumber = "1624854 (99e:60214)",
MRreviewer = "T. M. Liggett",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/28",
abstract = "We consider a hypersurface of dimension $d$ imbedded
in a $ d + 1$ dimensional space. For each $ x \in Z^d$,
let $ \eta_t(x) \in R$ be the height of the surface at
site $x$ at time $t$. At rate $1$ the $x$-th height is
updated to a random convex combination of the heights
of the `neighbors' of $x$. The distribution of the
convex combination is translation invariant and does
not depend on the heights. This motion, named the
random average process (RAP), is one of the linear
processes introduced by Liggett (1985). Special cases
of RAP are a type of smoothing process (when the convex
combination is deterministic) and the voter model (when
the convex combination concentrates on one site chosen
at random). We start the heights located on a
hyperplane passing through the origin but different
from the trivial one $ \eta (x) \equiv 0$. We show
that, when the convex combination is neither
deterministic nor concentrating on one site, the
variance of the height at the origin at time $t$ is
proportional to the number of returns to the origin of
a symmetric random walk of dimension $d$. Under mild
conditions on the distribution of the random convex
combination, this gives variance of the order of $ t^{1
/ 2}$ in dimension $ d = 1$, $ \log t$ in dimension $ d
= 2$ and bounded in $t$ in dimensions $ d \ge 3$. We
also show that for each initial hyperplane the process
as seen from the height at the origin converges to an
invariant measure on the hyper surfaces conserving the
initial asymptotic slope. The height at the origin
satisfies a central limit theorem. To obtain the
results we use a corresponding probabilistic cellular
automaton for which similar results are derived. This
automaton corresponds to the product of (infinitely
dimensional) independent random matrices whose rows are
independent.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "random average process, random surfaces, product of
random matrices, linear process, voter model, smoothing
process",
}
@Article{Feyel:1998:ASS,
author = "Denis Feyel and Arnaud {de La Pradelle}",
title = "On the approximate solutions of the {Stratonovitch}
equation",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "7:1--7:14",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-29",
ISSN = "1083-6489",
MRclass = "60H07 (60G17)",
MRnumber = "1624858 (99j:60075)",
MRreviewer = "Marco Ferrante",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/29",
abstract = "We present new methods for proving the convergence of
the classical approximations of the Stratonovitch
equation. We especially make use of the fractional
Liouville-valued Sobolev space $ W^{r, p}({\cal
J}_{\alpha, p}) $. We then obtain a support theorem for
the capacity $ c_{r, p} $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stratonovitch equations, Kolmogorov lemma, quasi-sure
analysis",
}
@Article{Capinski:1998:MAS,
author = "Marek Capi{\'n}ski and Nigel J. Cutland",
title = "Measure attractors for stochastic {Navier--Stokes}
equations",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "8:1--8:15",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-30",
ISSN = "1083-6489",
MRclass = "60H15 (35B40 35Q30 35R60)",
MRnumber = "1637081 (99f:60115)",
MRreviewer = "Wilfried Grecksch",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/30",
abstract = "We show existence of measure attractors for 2-D
stochastic Navier--Stokes equations with general
multiplicative noise.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "stochastic Navier--Stokes equations, measure
attractors",
}
@Article{Kurtz:1998:MPC,
author = "Thomas G. Kurtz",
title = "Martingale problems for conditional distributions of
{Markov} processes",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "9:1--9:29",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-31",
ISSN = "1083-6489",
MRclass = "60J25 (60G25 60G44 60J35)",
MRnumber = "1637085 (99k:60186)",
MRreviewer = "Amarjit Budhiraja",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/31",
abstract = "Let $X$ be a Markov process with generator $A$ and let
$ Y(t) = \gamma (X(t))$. The conditional distribution $
\pi_t$ of $ X(t)$ given $ \sigma (Y(s) \colon s \leq
t)$ is characterized as a solution of a filtered
martingale problem. As a consequence, we obtain a
generator/martingale problem version of a result of
Rogers and Pitman on Markov functions. Applications
include uniqueness of filtering equations,
exchangeability of the state distribution of
vector-valued processes, verification of
quasireversibility, and uniqueness for martingale
problems for measure-valued processes. New results on
the uniqueness of forward equations, needed in the
proof of uniqueness for the filtered martingale problem
are also presented.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "partial observation, conditional distribution,
filtering, forward equation, martingale problem, Markov
process, Markov function, quasireversibility,
measure-valued process",
}
@Article{Kesten:1998:AAW,
author = "Harry Kesten and Vladas Sidoravicius and Yu Zhang",
title = "Almost All Words Are Seen In Critical Site Percolation
On The Triangular Lattice",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "10:1--10:75",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-32",
ISSN = "1083-6489",
MRclass = "60K35",
MRnumber = "1637089 (99j:60155)",
MRreviewer = "Rahul Roy",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/32",
abstract = "We consider critical site percolation on the
triangular lattice, that is, we choose $ X(v) = 0 $ or
1 with probability 1/2 each, independently for all
vertices $v$ of the triangular lattice. We say that a
word $ (\xi_1, \xi_2, \dots) \in \{ 0, 1 \}^{\mathbb
{N}}$ is seen in the percolation configuration if there
exists a selfavoiding path $ (v_1, v_2, \dots)$ on the
triangular lattice with $ X(v_i) = \xi_i, i \ge 1$. We
prove that with probability 1 ``almost all'' words, as
well as all periodic words, except the two words $ (1,
1, 1, \dots)$ and $ (0, 0, 0, \dots)$, are seen.
``Almost all'' words here means almost all with respect
to the measure $ \mu_\beta $ under which the $ \xi_i$
are i.i.d. with $ \mu_\beta {\xi_i = 0} = 1 - \mu_\beta
{\xi_i = 1} = \beta $ (for an arbitrary $ 0 < \beta <
1$).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Percolation, Triangular lattice",
}
@Article{Yoo:1998:USS,
author = "Hyek Yoo",
title = "On the unique solvability of some nonlinear stochastic
{PDEs}",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "11:1--11:22",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-33",
ISSN = "1083-6489",
MRclass = "60H15 (35R60)",
MRnumber = "1639464 (99h:60126)",
MRreviewer = "Bohdan Maslowski",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/33",
abstract = "The Cauchy problem for 1-dimensional nonlinear
stochastic partial differential equations is studied.
The uniqueness and existence of solutions in $ c
H^2_p(T)$-space are proved.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic PDEs, Space of Bessel potentials, Embedding
theorems",
}
@Article{Fitzsimmons:1998:MPI,
author = "P. J. Fitzsimmons",
title = "{Markov} processes with identical bridges",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "12:1--12:12",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-34",
ISSN = "1083-6489",
MRclass = "60J25 (60J35)",
MRnumber = "1641066 (99h:60142)",
MRreviewer = "Kyle Siegrist",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/34",
abstract = "Let $X$ and $Y$ be time-homogeneous Markov processes
with common state space $E$, and assume that the
transition kernels of $X$ and $Y$ admit densities with
respect to suitable reference measures. We show that if
there is a time $ t > 0$ such that, for each $ x \in
E$, the conditional distribution of $ (X_s)_{0 \le s
\leq t}$, given $ X_0 = x = X_t$, coincides with the
conditional distribution of $ (Y_s)_{0 \leq s \leq t}$,
given $ Y_0 = x = Y_t$, then the infinitesimal
generators of $X$ and $Y$ are related by $ L^Y f =
\psi^{-1}L^X(\psi f) - \lambda f$, where $ \psi $ is an
eigenfunction of $ L^X$ with eigenvalue $ \lambda \in
{\bf R}$. Under an additional continuity hypothesis,
the same conclusion obtains assuming merely that $X$
and $Y$ share a ``bridge'' law for one triple $ (x, t,
y)$. Our work extends and clarifies a recent result of
I. Benjamini and S. Lee.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Bridge law, eigenfunction, transition density",
}
@Article{Davies:1998:LAE,
author = "Ian M. Davies",
title = "{Laplace} asymptotic expansions for {Gaussian}
functional integrals",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "13:1--13:19",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-35",
ISSN = "1083-6489",
MRclass = "60H05 (41A60)",
MRnumber = "1646472 (99i:60109)",
MRreviewer = "Kun Soo Chang",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/35",
abstract = "We obtain a Laplace asymptotic expansion, in orders of
$ \lambda $, of\par
$$ E^\rho_x \left \{ G(\lambda x) e^{- \lambda^{-2}
F(\lambda x)} \right \} $$
the expectation being with respect to a Gaussian
process. We extend a result of Pincus and build upon
the previous work of Davies and Truman. Our methods
differ from those of Ellis and Rosen in that we use the
supremum norm to simplify the application of the
result.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Gaussian processes, asymptotic expansions, functional
integrals",
}
@Article{Csaki:1998:LFS,
author = "Endre Cs{\'a}ki and Zhan Shi",
title = "Large favourite sites of simple random walk and the
{Wiener} process",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "14:1--14:31",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-36",
ISSN = "1083-6489",
MRclass = "60F15 (60G50 60J65)",
MRnumber = "1646468 (2000d:60050)",
MRreviewer = "Davar Khoshnevisan",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/36",
abstract = "Let $ U(n) $ denote the most visited point by a simple
symmetric random walk $ \{ S_k \}_{k \ge 0} $ in the
first $n$ steps. It is known that $ U(n)$ and $ m a
x_{0 \leq k \leq n} S_k$ satisfy the same law of the
iterated logarithm, but have different upper functions
(in the sense of P. L{\'e}vy). The distance between
them however turns out to be transient. In this paper,
we establish the exact rate of escape of this distance.
The corresponding problem for the Wiener process is
also studied.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Local time, favourite site, random walk, Wiener
process",
}
@Article{Montgomery-Smith:1998:CRM,
author = "Stephen Montgomery-Smith",
title = "Concrete Representation of Martingales",
journal = j-ELECTRON-J-PROBAB,
volume = "3",
pages = "15:1--15:15",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v3-37",
ISSN = "1083-6489",
MRclass = "60G42 (60G07 60H05)",
MRnumber = "1658686 (99k:60116)",
MRreviewer = "Dominique L{\'e}pingle",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/37",
abstract = "Let $ (f_n) $ be a mean zero vector valued martingale
sequence. Then there exist vector valued functions $
(d_n) $ from $ [0, 1]^n $ such that $ \int_0^1 d_n(x_1,
\dots, x_n) \, d x_n = 0 $ for almost all $ x_1, \dots,
x_{n - 1} $, and such that the law of $ (f_n) $ is the
same as the law of $ (\sum_{k = 1}^n d_k(x_1, \dots,
x_k)) $. Similar results for tangent sequences and
sequences satisfying condition (C.I.) are presented. We
also present a weaker version of a result of McConnell
that provides a Skorohod like representation for vector
valued martingales.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "martingale, concrete representation, tangent sequence,
condition (C.I.), UMD, Skorohod representation",
}
@Article{Pak:1998:RWF,
author = "Igor Pak",
title = "Random Walks On Finite Groups With Few Random
Generators",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "1:1--1:11",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-38",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/38",
abstract = "Let $G$ be a finite group. Choose a set $S$ of size
$k$ uniformly from $G$ and consider a lazy random walk
on the corresponding Cayley graph. We show that for
almost all choices of $S$ given $ k = 2 a \, \log_2
|G|$, $ a > 1$, this walk mixes in under $ m = 2 a \,
\log \frac {a}{a - 1} \log |G|$ steps. A similar result
was obtained earlier by Alon and Roichman and also by
Dou and Hildebrand using a different techniques. We
also prove that when sets are of size $ k = \log_2 |G|
+ O(\log \log |G|)$, $ m = O(\log^3 |G|)$ steps suffice
for mixing of the corresponding symmetric lazy random
walk. Finally, when $G$ is abelian we obtain better
bounds in both cases.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Random random walks on groups, random subproducts,
probabilistic method, separation distance",
}
@Article{Pak:1999:RWF,
author = "Igor Pak",
title = "Random walks on finite groups with few random
generators",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "1:1--1:11",
year = "1999",
CODEN = "????",
ISSN = "1083-6489",
MRclass = "60B15 (60G50)",
MRnumber = "1663526 (2000a:60008)",
MRreviewer = "Martin V. Hildebrand",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://www.math.washington.edu/~ejpecp/EjpVol4/paper1.abs.html",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Krylov:1999:AVF,
author = "N. V. Krylov",
title = "Approximating Value Functions for Controlled
Degenerate Diffusion Processes by Using Piece-Wise
Constant Policies",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "2:1--2:19",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-39",
ISSN = "1083-6489",
MRclass = "49L25 (35K65)",
MRnumber = "1668597 (2000b:49056)",
MRreviewer = "Martino Bardi",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/39",
abstract = "It is shown that value functions for controlled
degenerate diffusion processes can be approximated with
error of order $ h^{1 / 3} $ by using policies which
are constant on intervals $ [k h^2, (k + 1)h^2) $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Bellman's equations, fully nonlinear equations",
}
@Article{Bressaud:1999:DCN,
author = "Xavier Bressaud and Roberto Fern{\'a}ndez and Antonio
Galves",
title = "Decay of Correlations for Non-{H{\"o}lderian}
Dynamics. {A} Coupling Approach",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "3:1--3:19",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-40",
ISSN = "1083-6489",
MRclass = "60G10 (28D05 37A25 37A50)",
MRnumber = "1675304 (2000j:60049)",
MRreviewer = "Bernard Schmitt",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/40",
abstract = "We present an upper bound on the mixing rate of the
equilibrium state of a dynamical system defined by the
one-sided shift and a non H{\"o}lder potential of
summable variations. The bound follows from an
estimation of the relaxation speed of chains with
complete connections with summable decay, which is
obtained via a explicit coupling between pairs of
chains with different histories.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Dynamical systems, non-H{\"o}lder dynamics, m ixing
rate, chains with complete connections, relaxation
speed, coupling methods",
}
@Article{Dawson:1999:HIF,
author = "Donald A. Dawson and Andreas Greven",
title = "Hierarchically interacting {Fleming--Viot} processes
with selection and mutation: multiple space time scale
analysis and quasi-equilibria",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "4:1--4:81",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-41",
ISSN = "1083-6489",
MRclass = "60J70 (60K35 92D10 92D25)",
MRnumber = "1670873 (2000e:60139)",
MRreviewer = "Anton Wakolbinger",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/41",
abstract = "Genetic models incorporating resampling and migration
are now fairly well-understood. Problems arise in the
analysis, if both selection and mutation are
incorporated. This paper addresses some aspects of this
problem, in particular the analysis of the long-time
behaviour before the equilibrium is reached
(quasi-equilibrium, which is the time range of interest
in most applications).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Interacting Fleming--Viot processes, Renormalization
analysis, Selection, Mutation, Recombination",
}
@Article{Dohmen:1999:IIE,
author = "Klaus Dohmen",
title = "Improved Inclusion--Exclusion Identities and
Inequalities Based on a Particular Class of Abstract
Tubes",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "5:1--5:12",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-42",
ISSN = "1083-6489",
MRclass = "05A15 (05A19 05A20 68M15 90B25)",
MRnumber = "1684161 (2000a:05009)",
MRreviewer = "Stephen Tanny",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/42",
abstract = "Recently, Naiman and Wynn introduced the concept of an
abstract tube in order to obtain improved
inclusion-exclusion identities and inequalities that
involve much fewer terms than their classical
counterparts. In this paper, we introduce a particular
class of abstract tubes which plays an important role
with respect to chromatic polynomials and network
reliability. The inclusion-exclusion identities and
inequalities associated with this class simultaneously
generalize several well-known results such as Whitney's
broken circuit theorem, Shier's expression for the
reliability of a network as an alternating sum over
chains in a semilattice and Narushima's
inclusion-exclusion identity for posets. Moreover, we
show that under some restrictive assumptions a
polynomial time inclusion-exclusion algorithm can be
devised, which generalizes an important result of
Provan and Ball on network reliability.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Inclusion-exclusion, Bonferroni inequalities, sieve
formula, abstract tube, abstract simplicial complex,
partial order, chain, dynamic programming, graph
coloring, chromatic polynomial, broken circuit complex,
network reliability",
}
@Article{Dalang:1999:EMM,
author = "Robert C. Dalang",
title = "Extending the Martingale Measure Stochastic Integral
With Applications to Spatially Homogeneous S.P.D.E.'s",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "6:1--6:29",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-43",
ISSN = "1083-6489",
MRclass = "60H05 (35R60 60G15 60G48 60H15)",
MRnumber = "1684157 (2000b:60132)",
MRreviewer = "Marta Sanz Sol{\'e}",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/43",
abstract = "We extend the definition of Walsh's martingale measure
stochastic integral so as to be able to solve
stochastic partial differential equations whose Green's
function is not a function but a Schwartz distribution.
This is the case for the wave equation in dimensions
greater than two. Even when the integrand is a
distribution, the value of our stochastic integral
process is a real-valued martingale. We use this
extended integral to recover necessary and sufficient
conditions under which the linear wave equation driven
by spatially homogeneous Gaussian noise has a process
solution, and this in any spatial dimension. Under this
condition, the non-linear three dimensional wave
equation has a global solution. The same methods apply
to the damped wave equation, to the heat equation and
to various parabolic equations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "stochastic wave equation, stochastic heat equation,
Gaussian noise, process solution",
}
@Article{Arcones:1999:WCR,
author = "Miguel A. Arcones",
title = "Weak Convergence for the Row Sums of a Triangular
Array of Empirical Processes Indexed by a Manageable
Triangular Array of Functions",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "7:1--7:17",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-44",
ISSN = "1083-6489",
MRclass = "60B12 (60F17)",
MRnumber = "1684153 (2000c:60004)",
MRreviewer = "Lajos Horv{\'a}th",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/44",
abstract = "We study the weak convergence for the row sums of a
general triangular array of empirical processes indexed
by a manageable class of functions converging to an
arbitrary limit. As particular cases, we consider
random series processes and normalized sums of i.i.d.
random processes with Gaussian and stable limits. An
application to linear regression is presented. In this
application, the limit of the row sum of a triangular
array of empirical process is the mixture of a Gaussian
process with a random series process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Empirical processes, triangular arrays, manageable
classes",
}
@Article{Worms:1999:MDS,
author = "Julien Worms",
title = "Moderate deviations for stable {Markov} chains and
regression models",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "8:1--8:28",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-45",
ISSN = "1083-6489",
MRclass = "60F10 (60G10 62J02 62J05)",
MRnumber = "1684149 (2000b:60073)",
MRreviewer = "Peter Eichelsbacher",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/45",
abstract = "We prove moderate deviations principles for
\begin{itemize} \item unbounded additive functionals of
the form $ S_n = \sum_{j = 1}^n g(X^{(p)}_{j - 1}) $,
where $ (X_n)_{n \in N} $ is a stable $ R^d$-valued
functional autoregressive model of order $p$ with white
noise and stationary distribution $ \mu $, and $g$ is
an $ R^q$-valued Lipschitz function of order $ (r,
s)$;
\item the error of the least squares estimator (LSE) of
the matrix $ \theta $ in an $ R^d$-valued regression
model $ X_n = \theta^t \phi_{n - 1} + \epsilon_n$,
where $ (\epsilon_n)$ is a generalized Gaussian
noise.
\end{itemize} We apply these results to study the error
of the LSE for a stable $ R^d$-valued linear
autoregressive model of order $p$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Large and Moderate Deviations, Martingales, Markov
Chains, Least Squares Estimator for a regression
model",
}
@Article{Morters:1999:SSL,
author = "Peter M{\"o}rters and Narn-Rueih Shieh",
title = "Small scale limit theorems for the intersection local
times of {Brownian} motion",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "9:1--9:23",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-46",
ISSN = "1083-6489",
MRclass = "60G17 (28A78 60J55 60J65)",
MRnumber = "1690313 (2000e:60060)",
MRreviewer = "Yimin Xiao",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/46",
abstract = "In this paper we contribute to the investigation of
the fractal nature of the intersection local time
measure on the intersection of independent Brownian
paths. We particularly point out the difference in the
small scale behaviour of the intersection local times
in three-dimensional space and in the plane by studying
almost sure limit theorems motivated by the notion of
average densities introduced by Bedford and Fisher. We
show that in 3-space the intersection local time
measure of two paths has an average density of order
two with respect to the gauge function $ \varphi (r) =
r $, but in the plane, for the intersection local time
measure of p Brownian paths, the average density of
order two fails to converge. The average density of
order three, however, exists for the gauge function $
\varphi_p(r) = r^2 [\log (1 / r)]^p $. We also prove
refined versions of the above results, which describe
more precisely the fluctuations of the volume of small
balls around these gauge functions by identifying the
density distributions, or lacunarity distributions, of
the intersection local times.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion, intersection local time, Palm
distribution, average density, density distribution,
lacunarity distribution, logarithmic average",
}
@Article{Dembo:1999:TPT,
author = "Amir Dembo and Yuval Peres and Jay Rosen and Ofer
Zeitouni",
title = "Thick Points for Transient Symmetric Stable
Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "10:1--10:13",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-47",
ISSN = "1083-6489",
MRclass = "60J55 (60G52)",
MRnumber = "1690314 (2000f:60117)",
MRreviewer = "Larbi Alili",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/47",
abstract = "Let $ T(x, r) $ denote the total occupation measure of
the ball of radius $r$ centered at $x$ for a transient
symmetric stable processes of index $ b < d$ in $ R^d$
and $ K(b, d)$ denote the norm of the convolution with
its 0-potential density, considered as an operator on $
L^2 (B(0, 1), d x)$. We prove that as $r$ approaches 0,
almost surely $ \sup_{|x| \leq 1} T(x, r) / (r^b| \log
r|) \to b K(b, d)$. Furthermore, for any $ a \in (0, b
/ K(b, d))$, the Hausdorff dimension of the set of
``thick points'' $x$ for which $ \limsup_{r \to 0} T(x,
r) / (r^b | \log r|) = a$, is almost surely $ b - a /
K(b, d)$; this is the correct scaling to obtain a
nondegenerate ``multifractal spectrum'' for transient
stable occupation measure. The liminf scaling of $ T(x,
r)$ is quite different: we exhibit positive, finite,
non-random $ c(b, d), C(b, d)$, such that almost surely
$ c(b, d) < \sup_x \liminf_{r \to 0} T(x, r) / r^b <
C(b, d)$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stable process, occupation measure, multifractal
spectrum",
}
@Article{Pitman:1999:BMB,
author = "Jim Pitman",
title = "{Brownian} motion, bridge, excursion, and meander
characterized by sampling at independent uniform
times",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "11:1--11:33",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-48",
ISSN = "1083-6489",
MRclass = "60J65 (05A19 11B73)",
MRnumber = "1690315 (2000e:60137)",
MRreviewer = "G{\"o}tz Kersting",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/48;
http://www.math.washington.edu/~ejpecp/EjpVol4/paper11.abs.html",
abstract = "For a random process $X$ consider the random vector
defined by the values of $X$ at times $ 0 < U_{n, 1} <
\cdots {} < U_{n, n} < 1$ and the minimal values of $X$
on each of the intervals between consecutive pairs of
these times, where the $ U_{n, i}$ are the order
statistics of $n$ independent uniform $ (0, 1)$
variables, independent of $X$. The joint law of this
random vector is explicitly described when $X$ is a
Brownian motion. Corresponding results for Brownian
bridge, excursion, and meander are deduced by
appropriate conditioning. These descriptions yield
numerous new identities involving the laws of these
processes, and simplified proofs of various known
results, including Aldous's characterization of the
random tree constructed by sampling the excursion at
$n$ independent uniform times, Vervaat's transformation
of Brownian bridge into Brownian excursion, and
Denisov's decomposition of the Brownian motion at the
time of its minimum into two independent Brownian
meanders. Other consequences of the sampling formulae
are Brownian representations of various special
functions, including Bessel polynomials, some
hypergeometric polynomials, and the Hermite function.
Various combinatorial identities involving random
partitions and generalized Stirling numbers are also
obtained.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "alternating exponential random walk, uniform order
statistics, critical binary random tree, Vervaat's
transformation, random partitions, generalized Stirling
numbers, Bessel polynomials, McDonald function,
products of gamma variables, Hermite function",
}
@Article{Greven:1999:LBB,
author = "Andreas Greven and Achim Klenke and Anton
Wakolbinger",
title = "The Longtime Behavior of Branching Random Walk in a
Catalytic Medium",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "12:1--12:80",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-49",
ISSN = "1083-6489",
MRclass = "60K35 (60J80)",
MRnumber = "1690316 (2000a:60189)",
MRreviewer = "T. M. Liggett",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/49",
abstract = "Consider a countable collection of particles located
on a countable group, performing a critical branching
random walk where the branching rate of a particle is
given by a random medium fluctuating both in space and
time. Here we study the case where the time-space
random medium (called catalyst) is also a critical
branching random walk evolving autonomously while the
local branching rate of the reactant process is
proportional to the number of catalytic particles
present at a site. The catalyst process and the
reactant process typically have different underlying
motions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Branching random walk in random medium,
reactant-catalyst systems, interacting particle
Systems, random media",
}
@Article{Peligrad:1999:CSS,
author = "Magda Peligrad",
title = "Convergence of Stopped Sums of Weakly Dependent Random
Variables",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "13:1--13:13",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-50",
ISSN = "1083-6489",
MRclass = "60E15 (60F15 60G48)",
MRnumber = "1692676 (2000d:60033)",
MRreviewer = "Przemys{\l}aw Matu{\l}a",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/50",
abstract = "In this paper we investigate stopped partial sums for
weak dependent sequences.\par
In particular, the results are used to obtain new
maximal inequalities for strongly mixing sequences and
related almost sure results.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Partial sums, maximal inequalities, weak dependent
sequences, stopping times, amarts",
}
@Article{Steinsaltz:1999:RTC,
author = "David Steinsaltz",
title = "Random Time Changes for Sock-Sorting and Other
Stochastic Process Limit Theorems",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "14:1--14:25",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-51",
ISSN = "1083-6489",
MRclass = "60F05 (60C05 60K05)",
MRnumber = "1692672 (2000e:60038)",
MRreviewer = "Lars Holst",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/51",
abstract = "A common technique in the theory of stochastic process
is to replace a discrete time coordinate by a
continuous randomized time, defined by an independent
Poisson or other process. Once the analysis is complete
on this Poissonized process, translating the results
back to the original setting may be nontrivial. It is
shown here that, under fairly general conditions, if
the process $ S_n $ and the time change $ \phi_n $ both
converge, when normalized by the same constant, to
limit processes combined process $ S_n(\phi_n(t)) $
converges, when properly normalized, to a sum of the
limit of the original process, and the limit of the
time change multiplied by the derivative of $ E S_n $.
It is also shown that earlier results on the fine
structure of the maxima are preserved by these time
changes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "maximal inequalities, decoupling, Poissonization,
functional central limit theorem, sorting, random
allocations, auxiliary randomization, time change",
}
@Article{Pitman:1999:LMB,
author = "Jim Pitman and Marc Yor",
title = "The law of the maximum of a {Bessel} bridge",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "15:1--15:35",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-52",
ISSN = "1083-6489",
MRclass = "60J65 (33C10 60J60)",
MRnumber = "1701890 (2000j:60101)",
MRreviewer = "Endre Cs{\'a}ki",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/52;
http://www.math.washington.edu/~ejpecp/EjpVol4/paper15.abs.html",
abstract = "Let $ M_d $ be the maximum of a standard Bessel bridge
of dimension $d$. A series formula for $ P(M_d \leq a)$
due to Gikhman and Kiefer for $ d = 1, 2, \ldots $ is
shown to be valid for all real $ d > 0$. Various other
characterizations of the distribution of $ M_d$ are
given, including formulae for its Mellin transform,
which is an entire function. The asymptotic
distribution of $ M_d$ is described both as $d$ tends
to infinity and as $d$ tends to zero.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian bridge, Brownian excursion, Brownian scaling,
local time, Bessel process, zeros of Bessel functions,
Riemann zeta function",
}
@Article{Igloi:1999:LRD,
author = "E. Igl{\'o}i and G. Terdik",
title = "Long-range dependence through gamma-mixed
{Ornstein--Uhlenbeck} process",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "16:1--16:33",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-53",
ISSN = "1083-6489",
MRclass = "60H05 (60G15 60G18 60H10)",
MRnumber = "1713649 (2000m:60060)",
MRreviewer = "V. V. Anh",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/53",
abstract = "The limit process of aggregational models---(i) sum of
random coefficient AR(1) processes with independent
Brownian motion (BM) inputs and (ii) sum of AR(1)
processes with random coefficients of Gamma
distribution and with input of common BM's, ---proves
to be Gaussian and stationary and its transfer function
is the mixture of transfer functions of
Ornstein--Uhlenbeck (OU) processes by Gamma
distribution. It is called Gamma-mixed
Ornstein--Uhlenbeck process ($ \Gamma \mathsf {MOU}$).
For independent Poisson alternating $0$-$1$ reward
processes with proper random intensity it is shown that
the standardized sum of the processes converges to the
standardized $ \Gamma \mathsf {MOU}$ process. The $
\Gamma \mathsf {MOU}$ process has various interesting
properties and it is a new candidate for the successful
modelling of several Gaussian stationary data with
long-range dependence. Possible applications and
problems are also considered.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stationarity, Long-range dependence, Spectral
representation, Ornstein--Uhlenbeck process,
Aggregational model, Stochastic differentialequation,
Fractional Brownian motion input, Heart rate
variability",
}
@Article{Liptser:1999:MDT,
author = "R. Liptser and V. Spokoiny",
title = "Moderate Deviations Type Evaluation for Integral
Functionals of Diffusion Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "17:1--17:25",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-54",
ISSN = "1083-6489",
MRclass = "60F10 (60J60)",
MRnumber = "1741723 (2001j:60054)",
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/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/54",
abstract = "We establish a large deviations type evaluation for
the family of integral functionals.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "large deviations, moderate deviations, diffusion",
}
@Article{Fukushima:1999:SMC,
author = "Masatoshi Fukushima",
title = "On semi-martingale characterizations of functionals of
symmetric {Markov} processes",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "18:1--18:32",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-55",
ISSN = "1083-6489",
MRclass = "60J45 (31C25 60J55)",
MRnumber = "1741537 (2001b:60091)",
MRreviewer = "Zhen-Qing Chen",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/55",
abstract = "For a quasi-regular (symmetric) Dirichlet space $
({\cal E}, {\cal F}) $ and an associated symmetric
standard process $ (X_t, P_x) $, we show that, for $ u
i n {\cal F} $, the additive functional $ u^*(X_t) -
u^*(X_0) $ is a semimartingale if and only if there
exists an $ {\cal E}$-nest $ \{ F_n \} $ and positive
constants $ C_n$ such that $ \vert {\cal E}(u, v) \vert
\leq C_n \Vert v \Vert_\infty, v \in {\cal F}_{F_n,
b}.$ In particular, a signed measure resulting from the
inequality will be automatically smooth. One of the
variants of this assertion is applied to the distorted
Brownian motion on a closed subset of $ R^d$, giving
stochastic characterizations of BV functions and
Caccioppoli sets.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "quasi-regular Dirichlet form, strongly regular
representation, additive functionals, semimartingale,
smooth signed measure, BV function",
}
@Article{Getoor:1999:EGS,
author = "Ronald K. Getoor",
title = "An Extended Generator and {Schr{\"o}dinger}
Equations",
journal = j-ELECTRON-J-PROBAB,
volume = "4",
pages = "19:1--19:23",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v4-56",
ISSN = "1083-6489",
MRclass = "60J40 (60J25 60J35 60J45)",
MRnumber = "1741538 (2001c:60115)",
MRreviewer = "Zoran Vondra{\v{c}}ek",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/56",
abstract = "The generator of a Borel right process is extended so
that it maps functions to smooth measures. This
extension may be defined either probabilistically using
martingales or analytically in terms of certain kernels
on the state space of the process. Then the associated
Schr{\"o}dinger equation with a (signed) measure
serving as potential may be interpreted as an equation
between measures. In this context general existence and
uniqueness theorems for solutions are established.
These are then specialized to obtain more concrete
results in special situations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Markov processes, Schr{\"o}dinger equations,
generators, smooth measures",
}
@Article{Sharpe:1999:MRS,
author = "Michael Sharpe",
title = "Martingales on Random Sets and the Strong Martingale
Property",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "1:1--1:17",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-57",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/57",
abstract = "Let $X$ be a process defined on an optional random
set. The paper develops two different conditions on $X$
guaranteeing that it is the restriction of a uniformly
integrable martingale. In each case, it is supposed
that $X$ is the restriction of some special
semimartingale $Z$ with canonical decomposition $ Z = M
+ A$. The first condition, which is both necessary and
sufficient, is an absolute continuity condition on $A$.
Under additional hypotheses, the existence of a
martingale extension can be characterized by a strong
martingale property of $X$. Uniqueness of the extension
is also considered.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Martingale, random set, strong martingale property",
}
@Article{Camarri:1999:LDR,
author = "Michael Camarri and Jim Pitman",
title = "Limit Distributions and Random Trees Derived from the
Birthday Problem with Unequal Probabilities",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "2:1--2:18",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-58",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/58",
abstract = "Given an arbitrary distribution on a countable set,
consider the number of independent samples required
until the first repeated value is seen. Exact and
asymptotic formulae are derived for the distribution of
this time and of the times until subsequent repeats.
Asymptotic properties of the repeat times are derived
by embedding in a Poisson process. In particular,
necessary and sufficient conditions for convergence are
given and the possible limits explicitly described.
Under the same conditions the finite dimensional
distributions of the repeat times converge to the
arrival times of suitably modified Poisson processes,
and random trees derived from the sequence of
independent trials converge in distribution to an
inhomogeneous continuum random tree.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Repeat times, point process, Poisson embedding,
inhomogeneous continuum random tree, Rayleigh
distribution",
}
@Article{Bessaih:1999:SWA,
author = "Hakima Bessaih",
title = "Stochastic Weak Attractor for a Dissipative {Euler}
Equation",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "3:1--3:16",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-59",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/59",
abstract = "In this paper a nonautonomous dynamical system is
considered, a stochastic one that is obtained from the
dissipative Euler equation subject to a stochastic
perturbation, an additive noise. Absorbing sets have
been defined as sets that depend on time and attracts
from $ - \infty $. A stochastic weak attractor is
constructed in phase space with respect to two metrics
and is compact in the lower one.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Dissipative Euler Equation, random dynamical systems,
attractors",
}
@Article{Bertoin:1999:TCD,
author = "Jean Bertoin and Jim Pitman",
title = "Two Coalescents Derived from the Ranges of Stable
Subordinators",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "7:1--7:17",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-63",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/63",
abstract = "Let $ M_\alpha $ be the closure of the range of a
stable subordinator of index $ \alpha \in]0, 1 [ $.
There are two natural constructions of the $ M_{\alpha
} $'s simultaneously for all $ \alpha \in]0, 1 [ $, so
that $ M_{\alpha } \subseteq M_{\beta } $ for $ 0 <
\alpha < \beta < 1 $: one based on the intersection of
independent regenerative sets and one based on
Bochner's subordination. We compare the corresponding
two coalescent processes defined by the lengths of
complementary intervals of $ [0, 1] \backslash M_{1 -
\rho } $ for $ 0 < \rho < 1 $. In particular, we
identify the coalescent based on the subordination
scheme with the coalescent recently introduced by
Bolthausen and Sznitman.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "coalescent, stable, subordinator, Poisson--Dirichlet
distribution",
}
@Article{Khoshnevisan:2000:LRF,
author = "Davar Khoshnevisan and Yuval Peres and Yimin Xiao",
title = "Limsup Random Fractals",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "4:1--4:24",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-60",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/60",
abstract = "Orey and Taylor (1974) introduced sets of ``fast
points'' where Brownian increments are exceptionally
large, $ {\rm F}(\lambda) := \{ t \in [0, 1] \colon
\limsup_{h \to 0}{ | X(t + h) - X(t)| / \sqrt { 2h|
\log h|}} \ge \lambda \} $. They proved that for $
\lambda \in (0, 1] $, the Hausdorff dimension of $ {\rm
F}(\lambda) $ is $ 1 - \lambda^2 $ a.s. We prove that
for any analytic set $ E \subset [0, 1] $, the supremum
of the $ \lambda $ such that $E$ intersects $ {\rm
F}(\lambda)$ a.s. equals $ \sqrt {\text {dim}_p E }$,
where $ \text {dim}_p E$ is the {\em packing dimension}
of $E$. We derive this from a general result that
applies to many other random fractals defined by limsup
operations. This result also yields extensions of
certain ``fractal functional limit laws'' due to
Deheuvels and Mason (1994). In particular, we prove
that for any absolutely continuous function $f$ such
that $ f(0) = 0$ and the energy $ \int_0^1 |f'|^2 \, d
t $ is lower than the packing dimension of $E$, there
a.s. exists some $ t \in E$ so that $f$ can be
uniformly approximated in $ [0, 1]$ by normalized
Brownian increments $ s \mapsto [X(t + s h) - X(t)] /
\sqrt { 2h| \log h|}$; such uniform approximation is
a.s. impossible if the energy of $f$ is higher than the
packing dimension of $E$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Limsup random fractal, packing dimension, Hausdorff
dimension, Brownian motion, fast point",
}
@Article{Ichinose:2000:NED,
author = "Takashi Ichinose and Satoshi Takanobu",
title = "The Norm Estimate of the Difference Between the {Kac}
Operator and {Schr{\"o}dinger} Semigroup {II}: The
General Case Including the Relativistic Case",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "5:1--5:47",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-61",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/61",
abstract = "More thorough results than in our previous paper in
Nagoya Math. J. are given on the $ L_p$-operator norm
estimates for the Kac operator $ e^{-tV / 2} e^{-tH_0}
e^{-tV / 2}$ compared with the Schr{\"o}dinger
semigroup $ e^{-t(H_0 + V)}$. The Schr{\"o}dinger
operators $ H_0 + V$ to be treated in this paper are
more general ones associated with the L{\'e}vy process,
including the relativistic Schr{\"o}dinger operator.
The method of proof is probabilistic based on the
Feynman--Kac formula. It differs from our previous work
in the point of using {\em the Feynman--Kac formula\/}
not directly for these operators, but instead through
{\em subordination\/} from the Brownian motion, which
enables us to deal with all these operators in a
unified way. As an application of such estimates the
Trotter product formula in the $ L_p$-operator norm,
with error bounds, for these Schr{\"o}dinger semigroups
is also derived.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Schr{\"o}dinger operator, Schr{\"o}dinger semigroup,
relativistic Schr{\"o}dinger operator, Trotter product
formula, Lie--Trotter--Kato product formula,
Feynman--Kac formula, subordination of Brownian motion,
Kato's inequality",
}
@Article{Mikulevicius:2000:SEE,
author = "R. Mikulevicius and G. Valiukevicius",
title = "On Stochastic {Euler} equation in $ \mathbb {R}^d $",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "6:1--6:20",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-62",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/62",
abstract = "Following the Arnold--Marsden--Ebin approach, we prove
local (global in 2-D) existence and uniqueness of
classical (H{\"o}lder class) solutions of stochastic
Euler equation with random forcing.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic partial differential equations, Euler
equation",
}
@Article{Lawler:2000:SCH,
author = "Gregory Lawler",
title = "Strict Concavity of the Half Plane Intersection
Exponent for Planar {Brownian} Motion",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "8:1--8:33",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-64",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/64",
abstract = "The intersection exponents for planar Brownian motion
measure the exponential decay of probabilities of
nonintersection of paths. We study the intersection
exponent $ \xi (\lambda_1, \lambda_2) $ for Brownian
motion restricted to a half plane which by conformal
invariance is the same as Brownian motion restricted to
an infinite strip. We show that $ \xi $ is a strictly
concave function. This result is used in another paper
to establish a universality result for conformally
invariant intersection exponents.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion, intersection exponent",
}
@Article{Conlon:2000:HEE,
author = "Joseph Conlon and Ali Naddaf",
title = "On Homogenization Of Elliptic Equations With Random
Coefficients",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "9:1--9:58",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-65",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/65",
abstract = "In this paper, we investigate the rate of convergence
of the solution $ u_\varepsilon $ of the random
elliptic partial difference equation $
(\nabla^{\varepsilon *} a(x / \varepsilon, \omega)
\nabla^\varepsilon + 1)u_\varepsilon (x, \omega) = f(x)
$ to the corresponding homogenized solution. Here $ x
\in \varepsilon Z^d $, and $ \omega \in \Omega $
represents the randomness. Assuming that $ a(x) $'s are
independent and uniformly elliptic, we shall obtain an
upper bound $ \varepsilon^\alpha $ for the rate of
convergence, where $ \alpha $ is a constant which
depends on the dimension $ d \ge 2 $ and the deviation
of $ a(x, \omega) $ from the identity matrix. We will
also show that the (statistical) average of $
u_\varepsilon (x, \omega) $ and its derivatives decay
exponentially for large $x$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Homogenization, elliptic equations, random
environment, Euler-Lagrange equation",
}
@Article{Hu:2000:LCH,
author = "Yueyun Hu",
title = "The Laws of {Chung} and {Hirsch} for {Cauchy}'s
Principal Values Related to {Brownian} Local Times",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "10:1--10:16",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-66",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/66",
abstract = "Two Chung-type and Hirsch-type laws are established to
describe the liminf asymptotic behaviours of the
Cauchy's principal values related to Brownian local
times. These results are generalized to a class of
Brownian additive functionals.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Principal values, Brownian additive functional, liminf
asymptotic behaviours",
}
@Article{Feyel:2000:ARP,
author = "D. Feyel and A. {de La Pradelle}",
title = "The Abstract {Riemannian} Path Space",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "11:1--11:17",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-67",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/67",
abstract = "On the Wiener space $ \Omega $, we introduce an
abstract Ricci process $ A_t $ and a pseudo-gradient $
F \rightarrow {F}^\sharp $ which are compatible through
an integration by parts formula. They give rise to a $
\sharp $-Sobolev space on $ \Omega $, logarithmic
Sobolev inequalities, and capacities, which are tight
on Hoelder compact sets of $ \Omega $. These are then
applied to the path space over a Riemannian manifold.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Wiener space, Sobolev spaces, Bismut--Driver formula,
Logarithmic Sobolev inequality, Capacities, Riemannian
manifold path space",
}
@Article{Schweinsberg:2000:CSM,
author = "Jason Schweinsberg",
title = "Coalescents with Simultaneous Multiple Collisions",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "12:1--12:50",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-68",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/68",
abstract = "We study a family of coalescent processes that undergo
``simultaneous multiple collisions, '' meaning that
many clusters of particles can merge into a single
cluster at one time, and many such mergers can occur
simultaneously. This family of processes, which we
obtain from simple assumptions about the rates of
different types of mergers, essentially coincides with
a family of processes that Mohle and Sagitov obtain as
a limit of scaled ancestral processes in a population
model with exchangeable family sizes. We characterize
the possible merger rates in terms of a single measure,
show how these coalescents can be constructed from a
Poisson process, and discuss some basic properties of
these processes. This work generalizes some work of
Pitman, who provides similar analysis for a family of
coalescent processes in which many clusters can
coalesce into a single cluster, but almost surely no
two such mergers occur simultaneously.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "coalescence, ancestral processes, Poisson point
processes, Markov processes, exchangeable random
partitions",
}
@Article{Krylov:2000:SS,
author = "N. Krylov",
title = "{SPDEs} in {$ L_q((0, \tau], L_p) $} Spaces",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "13:1--13:29",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-69",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/69",
abstract = "Existence and uniqueness theorems are presented for
evolutional stochastic partial differential equations
of second order in $ L_p$-spaces with weights allowing
derivatives of solutions to blow up near the boundary.
It is allowed for the powers of summability with
respect to space and time variables to be different.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic partial differential equations, Sobolev
spaces with weights",
}
@Article{Lyne:2000:TWC,
author = "Owen Lyne",
title = "Travelling Waves for a Certain First-Order Coupled
{PDE} System",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "14:1--14:40",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-70",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/70",
abstract = "This paper concentrates on a particular first-order
coupled PDE system. It provides both a detailed
treatment of the {\em existence\/} and {\em
uniqueness\/} of monotone travelling waves to various
equilibria, by differential-equation theory and by
probability theory and a treatment of the corresponding
hyperbolic initial-value problem, by analytic methods.
The initial-value problem is studied using
characteristics to show existence and uniqueness of a
bounded solution for bounded initial data (subject to
certain smoothness conditions). The concept of {\em
weak\/} solutions to partial differential equations is
used to rigorously examine bounded initial data with
jump discontinuities. For the travelling wave problem
the differential-equation treatment makes use of a
shooting argument and explicit calculations of the
eigenvectors of stability matrices. The probabilistic
treatment is careful in its proofs of {\em
martingale\/} (as opposed to merely local-martingale)
properties. A modern {\em change-of-measure
technique\/} is used to obtain the best lower bound on
the speed of the monotone travelling wave --- with
Heaviside initial conditions the solution converges to
an approximate travelling wave of that speed (the
solution tends to one ahead of the wave-front and to
zero behind it). Waves to different equilibria are
shown to be related by Doob $h$-transforms. {\em
Large-deviation theory\/} provides heuristic links
between alternative descriptions of minimum wave
speeds, rigorous algebraic proofs of which are
provided.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Travelling waves, Martingales, Branching processes",
}
@Article{Kopp:2000:CIM,
author = "P. Kopp and Volker Wellmann",
title = "Convergence in Incomplete Market Models",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "15:1--15:26",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-71",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/71",
abstract = "The problem of pricing and hedging of contingent
claims in incomplete markets has led to the development
of various valuation methodologies. This paper examines
the mean-variance approach to risk-minimisation and
shows that it is robust under the convergence from
discrete- to continuous-time market models. This
property yields new convergence results for option
prices, trading strategies and value processes in
incomplete market models. Techniques from nonstandard
analysis are used to develop new results for the
lifting property of the minimal martingale density and
risk-minimising strategies. These are applied to a
number of incomplete market models:\par
It is shown that the convergence of the underlying
models implies the convergence of strategies and value
processes for multinomial models and approximations of
the Black--Scholes model by direct discretisation of
the price process. The concept of $ D^2$-convergence is
extended to these classes of models, including the
construction of discretisation schemes. This yields new
standard convergence results for these models.\par
For ease of reference a summary of the main results
from nonstandard analysis in the context of stochastic
analysis is given as well as a brief introduction to
mean-variance hedging and pricing.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Financial models, incomplete markets",
}
@Article{Goldsheid:2000:ECA,
author = "Ilya Goldsheid and Boris Khoruzhenko",
title = "Eigenvalue Curves of Asymmetric Tridiagonal Matrices",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "16:1--16:28",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-72",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/72",
abstract = "Random Schr{\"o}dinger operators with imaginary vector
potentials are studied in dimension one. These
operators are non-Hermitian and their spectra lie in
the complex plane. We consider the eigenvalue problem
on finite intervals of length $n$ with periodic
boundary conditions and describe the limit eigenvalue
distribution when $n$ goes to infinity. We prove that
this limit distribution is supported by curves in the
complex plane. We also obtain equations for these
curves and for the corresponding eigenvalue density in
terms of the Lyapunov exponent and the integrated
density of states of a ``reference'' symmetric
eigenvalue problem. In contrast to these results, the
spectrum of the limit operator in $ \ell^2 (Z)$ is a
two dimensional set which is not approximated by the
spectra of the finite-interval operators.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Random matrix, Schr{\"o}dinger operator, Lyapunov
exponent, eigenvalue distribution, complex
eigenvalue.",
}
@Article{Geiger:2000:PPP,
author = "Jochen Geiger",
title = "{Poisson} point process limits in size-biased
{Galton--Watson} trees",
journal = j-ELECTRON-J-PROBAB,
volume = "5",
pages = "17:1--17:12",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v5-73",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/73",
abstract = "Consider a critical binary continuous-time
Galton--Watson tree size-biased according to the number
of particles at time $t$. Decompose the population at
$t$ according to the particles' degree of relationship
with a distinguished particle picked purely at random
from those alive at $t$. Keeping track of the times
when the different families grow out of the
distinguished line of descent and the related family
sizes at $t$, we represent this relationship structure
as a point process in a time-size plane. We study
limits of these point processes in the single- and some
multitype case.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Galton--Watson process, random tree, point process,
limit laws",
}
@Article{Sengupta:2000:FPD,
author = "Arindam Sengupta and Anish Sarkar",
title = "Finitely Polynomially Determined {L{\'e}vy}
Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "7:1--7:22",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-80",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/80",
abstract = "A time-space harmonic polynomial for a continuous-time
process $ X = \{ X_t \colon t \ge 0 \} $ is a
two-variable polynomial $P$ such that $ \{ P(t, X_t)
\colon t \ge 0 \} $ is a martingale for the natural
filtration of $X$. Motivated by L{\'e}vy's
characterisation of Brownian motion and Watanabe's
characterisation of the Poisson process, we look for
classes of processes with reasonably general path
properties in which a characterisation of those members
whose laws are determined by a finite number of such
polynomials is available. We exhibit two classes of
processes, the first containing the L{\'e}vy processes,
and the second a more general class of additive
processes, with this property and describe the
respective characterisations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "L{\'e}vy process, additive process, L{\'e}vy's
characterisation, L{\'e}vy measure, Kolmogorov
measure",
}
@Article{Mountford:2001:NLB,
author = "Thomas Mountford",
title = "A Note on Limiting Behaviour of Disastrous Environment
Exponents",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "1:1--1:10",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-74",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/74",
abstract = "We consider a random walk on the $d$-dimensional
lattice and investigate the asymptotic probability of
the walk avoiding a ``disaster'' (points put down
according to a regular Poisson process on space-time).
We show that, given the Poisson process points, almost
surely, the chance of surviving to time $t$ is like $
e^{- \alpha \log (\frac 1k) t } $, as $t$ tends to
infinity if $k$, the jump rate of the random walk, is
small.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Random walk, disaster point, Poisson process",
}
@Article{Su:2001:DCD,
author = "Francis Su",
title = "Discrepancy Convergence for the Drunkard's Walk on the
Sphere",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "2:1--2:20",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-75",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/75",
abstract = "We analyze the drunkard's walk on the unit sphere with
step size $ \theta $ and show that the walk converges
in order $ C / \sin^2 (\theta) $ steps in the
discrepancy metric ($C$ a constant). This is an
application of techniques we develop for bounding the
discrepancy of random walks on Gelfand pairs generated
by bi-invariant measures. In such cases, Fourier
analysis on the acting group admits tractable
computations involving spherical functions. We advocate
the use of discrepancy as a metric on probabilities for
state spaces with isometric group actions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "discrepancy, random walk, Gelfand pairs, homogeneous
spaces, Legendre polynomials",
}
@Article{Bai:2001:LTN,
author = "Zhi-Dong Bai and Hsien-Kuei Hwang and Wen-Qi Liang and
Tsung-Hsi Tsai",
title = "Limit Theorems for the Number of Maxima in Random
Samples from Planar Regions",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "3:1--3:41",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-76",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/76",
abstract = "We prove that the number of maximal points in a random
sample taken uniformly and independently from a convex
polygon is asymptotically normal in the sense of
convergence in distribution. Many new results for other
planar regions are also derived. In particular, precise
Poisson approximation results are given for the number
of maxima in regions bounded above by a nondecreasing
curve.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Maximal points, multicriterial optimization, central
limit theorems, Poisson approximations, convex
polygons",
}
@Article{Kesten:2001:PAW,
author = "Harry Kesten and Vladas Sidoravicius and Yu Zhang",
title = "Percolation of Arbitrary words on the Close-Packed
Graph of $ \mathbb {Z}^2 $",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "4:1--4:27",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-77",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/77",
abstract = "Let $ {\mathbb {Z}}^2_{cp} $ be the close-packed graph
of $ \mathbb {Z}^2 $, that is, the graph obtained by
adding to each face of $ \mathbb {Z}^2 $ its diagonal
edges. We consider site percolation on $ \mathbb
{Z}^2_{cp} $, namely, for each $v$ we choose $ X(v) =
1$ or 0 with probability $p$ or $ 1 - p$, respectively,
independently for all vertices $v$ of $ \mathbb
{Z}^2_{cp}$. We say that a word $ (\xi_1, \xi_2, \dots)
\in \{ 0, 1 \}^{\mathbb {N}}$ is seen in the
percolation configuration if there exists a
selfavoiding path $ (v_1, v_2, \dots)$ on $ \mathbb
{Z}^2_{cp}$ with $ X(v_i) = \xi_i, i \ge 1$. $
p_c(\mathbb {Z}^2, \text {site})$ denotes the critical
probability for site-percolation on $ \mathbb {Z}^2$.
We prove that for each fixed $ p \in \big (1 -
p_c(\mathbb {Z}^2, \text {site}), p_c(\mathbb {Z}^2,
\text {site}) \big)$, with probability 1 all words are
seen. We also show that for some constants $ C_i > 0$
there is a probability of at least $ C_1$ that all
words of length $ C_0 n^2$ are seen along a path which
starts at a neighbor of the origin and is contained in
the square $ [ - n, n]^2$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Percolation, close-packing",
}
@Article{Flandoli:2001:SSS,
author = "Franco Flandoli and Marco Romito",
title = "Statistically Stationary Solutions to the {$3$D}
{Navier--Stokes} Equations do not show Singularities",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "5:1--5:15",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-78",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/78",
abstract = "If $ \mu $ is a probability measure on the set of
suitable weak solutions of the 3D Navier--Stokes
equations, invariant for the time-shift, with finite
mean dissipation rate, then at every time $t$ the set
of singular points is empty $ \mu $-a.s. The existence
of a measure $ \mu $ with the previous properties is
also proved; it may describe a turbulent asymptotic
regime.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Navier--Stokes equations, suitable weak solutions,
stationary solutions",
}
@Article{DeSantis:2001:SIP,
author = "Emilio {De Santis}",
title = "Strict Inequality for Phase Transition between
Ferromagnetic and Frustrated Systems",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "6:1--6:27",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-79",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/79",
abstract = "We consider deterministic and disordered frustrated
systems in which we can show some strict inequalities
with respect to related ferromagnetic systems. A case
particularly interesting is the Edwards--Anderson
spin-glass model in which it is possible to determine a
region of uniqueness of the Gibbs measure, which is
strictly larger than the region of uniqueness for the
related ferromagnetic system. We analyze also
deterministic systems with $ |J_b| \in [J_A, J_B] $
where $ 0 < J_A \leq J_B < \infty $, for which we prove
strict inequality for the critical points of the
related FK model. The results are obtained for the
Ising models but some extensions to Potts models are
possible.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Phase transition, Ising model, disordered systems,
stochastic order",
}
@Article{Heck:2001:PLD,
author = "Matthias Heck and Fa{\"\i}za Maaouia",
title = "The Principle of Large Deviations for Martingale
Additive Functionals of Recurrent {Markov} Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "8:1--8:26",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-81",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/81",
abstract = "We give a principle of large deviations for a
generalized version of the strong central limit
theorem. This generalized version deals with martingale
additive functionals of a recurrent Markov process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Central Limit Theorem (CLT), Large Deviations
Principle (LDP), Markov Processes, Autoregressive Model
(AR1), Positive Recurrent Processes, Martingale
Additive Functional (MAF)",
}
@Article{Barlow:2001:TDA,
author = "Martin Barlow and Takashi Kumagai",
title = "Transition Density Asymptotics for Some Diffusion
Processes with Multi-Fractal Structures",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "9:1--9:23",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-82",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/82",
abstract = "We study the asymptotics as $ t \to 0 $ of the
transition density of a class of $ \mu $-symmetric
diffusions in the case when the measure $ \mu $ has a
multi-fractal structure. These diffusions include
singular time changes of Brownian motion on the unit
cube.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Diffusion process, heat equation, transition density,
spectral dimension, multi-fractal",
}
@Article{Pemantle:2001:WDB,
author = "Robin Pemantle and Yuval Peres and Jim Pitman and Marc
Yor",
title = "Where Did the {Brownian} Particle Go?",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "10:1--10:22",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-83",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/83",
abstract = "Consider the radial projection onto the unit sphere of
the path a $d$-dimensional Brownian motion $W$, started
at the center of the sphere and run for unit time.
Given the occupation measure $ \mu $ of this projected
path, what can be said about the terminal point $
W(1)$, or about the range of the original path? In any
dimension, for each Borel set $A$ in $ S^{d - 1}$, the
conditional probability that the projection of $ W(1)$
is in $A$ given $ \mu (A)$ is just $ \mu (A)$.
Nevertheless, in dimension $ d \ge 3$, both the range
and the terminal point of $W$ can be recovered with
probability 1 from $ \mu $. In particular, for $ d \ge
3$ the conditional law of the projection of $ W(1)$
given $ \mu $ is not $ \mu $. In dimension 2 we
conjecture that the projection of $ W(1)$ cannot be
recovered almost surely from $ \mu $, and show that the
conditional law of the projection of $ W(1)$ given $
\mu $ is not $ m u$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion, conditional distribution of a path
given its occupation measure, radial projection",
}
@Article{Fill:2001:MTM,
author = "James Fill and Clyde {Schoolfield, Jr.}",
title = "Mixing Times for {Markov} Chains on Wreath Products
and Related Homogeneous Spaces",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "11:1--11:22",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-84",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/84",
abstract = "We develop a method for analyzing the mixing times for
a quite general class of Markov chains on the complete
monomial group $ G \wr S_n $ and a quite general class
of Markov chains on the homogeneous space $ (G \wr S_n)
/ (S_r \times S_{n - r}) $. We derive an exact formula
for the $ L^2 $ distance in terms of the $ L^2 $
distances to uniformity for closely related random
walks on the symmetric groups $ S_j $ for $ 1 \leq j
\leq n $ or for closely related Markov chains on the
homogeneous spaces $ S_{i + j} / (S_i \times S_j) $ for
various values of $i$ and $j$, respectively. Our
results are consistent with those previously known, but
our method is considerably simpler and more general.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Markov chain, random walk, rate of convergence to
stationarity, mixing time, wreath product,
Bernoulli--Laplace diffusion, complete monomial group,
hyperoctahedral group, homogeneous space, M{\"o}bius
inversion.",
}
@Article{Mikulevicius:2001:NKT,
author = "R. Mikulevicius and B. Rozovskii",
title = "A Note on {Krylov}'s {$ L_p $}-Theory for Systems of
{SPDEs}",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "12:1--12:35",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-85",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/85",
abstract = "We extend Krylov's $ L_p$-solvability theory to the
Cauchy problem for systems of parabolic stochastic
partial differential equations. Some additional
integrability and regularity properties are also
presented.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic partial differential equations, Cauchy
problem",
}
@Article{Nishioka:2001:BCO,
author = "Kunio Nishioka",
title = "Boundary Conditions for One-Dimensional Biharmonic
Pseudo Process",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "13:1--13:27",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-86",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/86",
abstract = "We study boundary conditions for a stochastic pseudo
processes corresponding to the biharmonic operator. The
biharmonic pseudo process ({\em BPP\/} for short). is
composed, in a sense, of two different particles, a
monopole and a dipole. We show how an initial-boundary
problems for a 4-th order parabolic differential
equation can be represented by {\em BPP\/} with various
boundary conditions for the two particles: killing,
reflection and stopping.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Boundary conditions for biharmonic pseudo process,
killing, reflection, stopping",
}
@Article{Miermont:2001:OAC,
author = "Gr{\'e}gory Miermont",
title = "Ordered Additive Coalescent and Fragmentations
Associated to {L{\'e}vy} Processes with No Positive
Jumps",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "14:1--14:33",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-87",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/87",
abstract = "We study here the fragmentation processes that can be
derived from L{\'e}vy processes with no positive jumps
in the same manner as in the case of a Brownian motion
(cf. Bertoin [4]). One of our motivations is that such
a representation of fragmentation processes by
excursion-type functions induces a particular order on
the fragments which is closely related to the
additivity of the coalescent kernel. We identify the
fragmentation processes obtained this way as a mixing
of time-reversed extremal additive coalescents by
analogy with the work of Aldous and Pitman [2], and we
make its semigroup explicit.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Additive-coalescent, fragmentation, L{\'e}vy
processes, processes with exchangeable increments",
}
@Article{Jonasson:2001:DPM,
author = "Johan Jonasson",
title = "On Disagreement Percolation and Maximality of the
Critical Value for iid Percolation",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "15:1--15:13",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-88",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/88",
abstract = "Two different problems are
studied:\par
\begin{itemize} \item For an infinite locally finite
connected graph $G$, let $ p_c(G)$ be the critical
value for the existence of an infinite cluster in iid
bond percolation on $G$ and let $ P_c = \sup \{ p_c(G)
\colon G \text { transitive }, p_c(G) < 1 \} $. Is $
P_c < 1$ ? \item Let $G$ be transitive with $ p_c(G) <
1$, take $ p \in [0, 1]$ and let $X$ and $Y$ be iid
bond percolations on $G$ with retention parameters $ (1
+ p) / 2$ and $ (1 - p) / 2$ respectively. Is there a $
q < 1$ such that $ p > q$ implies that for any monotone
coupling $ (X', Y')$ of $X$ and $Y$ the edges for which
$ X'$ and $ Y'$ disagree form infinite connected
component(s) with positive probability? Let $ p_d(G)$
be the infimum of such $q$'s (including $ q = 1$) and
let $ P_d = \sup \{ p_d(G) \colon G \text { transitive
}, p_c(G) < 1 \} $. Is the stronger statement $ P_d <
1$ true? On the other hand: Is it always true that $
p_d(G) > p_c (G)$ ? \end{itemize}\par
It is shown that if one restricts attention to
biregular planar graphs then these two problems can be
treated in a similar way and all the above questions
are positively answered. We also give examples to show
that if one drops the assumption of transitivity, then
the answer to the above two questions is no.
Furthermore it is shown that for any bounded-degree
bipartite graph $G$ with $ p_c(G) < 1$ one has $ p_c(G)
< p_d(G)$. Problem (2) arises naturally from [6] where
an example is given of a coupling of the distinct plus-
and minus measures for the Ising model on a
quasi-transitive graph at super-critical inverse
temperature. We give an example of such a coupling on
the $r$-regular tree, $ {\bf T}_r$, for $ r > 1$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "coupling, Ising model, random-cluster model,
transitive graph, planar graph",
}
@Article{DelMoral:2001:CDG,
author = "P. {Del Moral} and M. Kouritzin and L. Miclo",
title = "On a Class of Discrete Generation Interacting Particle
Systems",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "16:1--16:26",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-89",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/89",
abstract = "The asymptotic behavior of a general class of discrete
generation interacting particle systems is discussed.
We provide $ L_p$-mean error estimates for their
empirical measure on path space and present sufficient
conditions for uniform convergence of the particle
density profiles with respect to the time parameter.
Several examples including mean field particle models,
genetic schemes and McKean's Maxwellian gases will also
be given. In the context of Feynman--Kac type limiting
distributions we also prove central limit theorems and
we start a variance comparison for two generic particle
approximating models.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Interacting particle systems, genetic algorithms,
Feynman--Kac formulas, stochastic approximations,
central limit theorem",
}
@Article{Kurtz:2001:SSF,
author = "Thomas Kurtz and Richard Stockbridge",
title = "Stationary Solutions and Forward Equations for
Controlled and Singular Martingale Problems",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "17:1--17:52",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-90",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/90",
abstract = "Stationary distributions of Markov processes can
typically be characterized as probability measures that
annihilate the generator in the sense that $ | \int_E A
f d \mu = 0 $ for $ f \in {\cal D}(A) $; that is, for
each such $ \mu $, there exists a stationary solution
of the martingale problem for $A$ with marginal
distribution $ \mu $. This result is extended to models
corresponding to martingale problems that include
absolutely continuous and singular (with respect to
time) components and controls. Analogous results for
the forward equation follow as a corollary.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "singular controls, stationary processes, Markov
processes, martingale problems, forward equations,
constrained Markov processes",
}
@Article{Atar:2001:IWT,
author = "Rami Atar",
title = "Invariant Wedges for a Two-Point Reflecting {Brownian}
Motion and the ``Hot Spots'' Problem",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "18:1--18:19",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-91",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/91",
abstract = "We consider domains $D$ of $ R^d$, $ d \ge 2$ with the
property that there is a wedge $ V \subset R^d$ which
is left invariant under all tangential projections at
smooth portions of $ \partial D$. It is shown that the
difference between two solutions of the Skorokhod
equation in $D$ with normal reflection, driven by the
same Brownian motion, remains in $V$ if it is initially
in $V$. The heat equation on $D$ with Neumann boundary
conditions is considered next. It is shown that the
cone of elements $u$ of $ L^2 (D)$ satisfying $ u(x) -
u(y) \ge 0$ whenever $ x - y \in V$ is left invariant
by the corresponding heat semigroup. Positivity
considerations identify an eigenfunction corresponding
to the second Neumann eigenvalue as an element of this
cone. For $ d = 2$ and under further assumptions,
especially convexity of the domain, this eigenvalue is
simple.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Reflecting Brownian motion, Neumann eigenvalue
problem, convex domains",
}
@Article{Lambert:2001:JLA,
author = "Amaury Lambert",
title = "The Joint Law of Ages and Residual Lifetimes for Two
Schemes of Regenerative Sets",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "19:1--19:23",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-92",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/92",
abstract = "We are interested in the component intervals of the
complements of a monotone sequence $ R_n \subseteq
\dots \subseteq R_1 $ of regenerative sets, for two
natural embeddings. One is based on Bochner's
subordination, and one on the intersection of
independent regenerative sets. For each scheme, we
study the joint law of the so-called ages and residual
lifetimes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Multivariate renewal theory, regenerative sets,
subordinator, random covering intervals",
}
@Article{Lyne:2001:WSS,
author = "Owen Lyne and David Williams",
title = "Weak Solutions for a Simple Hyperbolic System",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "20:1--20:21",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-93",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/93",
abstract = "The model studied concerns a simple first-order {\em
hyperbolic\/} system. The solutions in which one is
most interested have discontinuities which persist for
all time, and therefore need to be interpreted as {\em
weak\/} solutions. We demonstrate existence and
uniqueness for such weak solutions, identifying a
canonical `{\em exact\/}' solution which is {\em
everywhere\/} defined. The direct method used is guided
by the theory of measure-valued diffusions. The method
is more effective than the method of characteristics,
and has the advantage that it leads immediately to the
McKean representation without recourse to It{\^o}'s
formula. We then conduct computer studies of our model,
both by integration schemes (which {\em do\/} use
characteristics) and by `random simulation'.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Weak solutions, Travelling waves, Martingales,
Branching processses",
}
@Article{Kolokoltsov:2001:SDF,
author = "Vassili Kolokoltsov",
title = "Small Diffusion and Fast Dying Out Asymptotics for
Superprocesses as Non-{Hamiltonian} Quasiclassics for
Evolution Equations",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "21:1--21:16",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-94",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/94",
abstract = "The small diffusion and fast dying out asymptotics is
calculated for nonlinear equations of a class of
superprocesses on manifolds, and the corresponding
logarithmic limit of the solution is shown to be given
by a solution of a certain problem of calculus of
variations with a non-additive (and non-integral)
functional.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Dawson--Watanabe superprocess, reaction diffusion
equation, logarithmic limit, small diffusion
asymptotics, curvilinear Ornstein--Uhlenbeck process",
}
@Article{Telcs:2001:LSG,
author = "Andras Telcs",
title = "Local Sub-{Gaussian} Estimates on Graphs: The Strongly
Recurrent Case",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "22:1--22:33",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-95",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/95",
abstract = "This paper proves upper and lower off-diagonal,
sub-Gaussian transition probabilities estimates for
strongly recurrent random walks under sufficient and
necessary conditions. Several equivalent conditions are
given showing their particular role and influence on
the connection between the sub-Gaussian estimates,
parabolic and elliptic Harnack inequality.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Random walks, potential theory, Harnack inequality,
reversible Markov chains",
}
@Article{Benjamini:2001:RDL,
author = "Itai Benjamini and Oded Schramm",
title = "Recurrence of Distributional Limits of Finite Planar
Graphs",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "23:1--23:13",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-96",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/96",
abstract = "Suppose that $ G_j $ is a sequence of finite connected
planar graphs, and in each $ G_j $ a special vertex,
called the root, is chosen randomly-uniformly. We
introduce the notion of a distributional limit $G$ of
such graphs. Assume that the vertex degrees of the
vertices in $ G_j$ are bounded, and the bound does not
depend on $j$. Then after passing to a subsequence, the
limit exists, and is a random rooted graph $G$. We
prove that with probability one $G$ is recurrent. The
proof involves the Circle Packing Theorem. The
motivation for this work comes from the theory of
random spherical triangulations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Random triangulations, random walks, mass transport,
circle packing, volume growth",
}
@Article{Lototsky:2001:LSP,
author = "Sergey Lototsky",
title = "Linear Stochastic Parabolic Equations, Degenerating on
the Boundary of a Domain",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "24:1--24:14",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-97",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/97",
abstract = "A class of linear degenerate second-order parabolic
equations is considered in arbitrary domains. It is
shown that these equations are solvable using special
weighted Sobolev spaces in essentially the same way as
the non-degenerate equations in $ R^d $ are solved
using the usual Sobolev spaces. The main advantages of
this Sobolev-space approach are less restrictive
conditions on the coefficients of the equation and
near-optimal space-time regularity of the solution.
Unlike previous works on degenerate equations, the
results cover both classical and distribution solutions
and allow the domain to be bounded or unbounded without
any smoothness assumptions about the boundary. An
application to nonlinear filtering of diffusion
processes is discussed.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "$L_p$ estimates, Weighted spaces, Nonlinear
filtering",
}
@Article{Dawson:2001:SDS,
author = "Donald Dawson and Zenghu Li and Hao Wang",
title = "Superprocesses with Dependent Spatial Motion and
General Branching Densities",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "25:1--25:33",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-98",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/98",
abstract = "We construct a class of superprocesses by taking the
high density limit of a sequence of
interacting-branching particle systems. The spatial
motion of the superprocess is determined by a system of
interacting diffusions, the branching density is given
by an arbitrary bounded non-negative Borel function,
and the superprocess is characterized by a martingale
problem as a diffusion process with state space $
M({\bf R}) $, improving and extending considerably the
construction of Wang (1997, 1998). It is then proved in
a special case that a suitable rescaled process of the
superprocess converges to the usual super Brownian
motion. An extension to measure-valued branching
catalysts is also discussed.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "superprocess, interacting-branching particle system,
diffusion process, martingale problem, dual process,
rescaled limit, measure-valued catalyst",
}
@Article{Feyel:2001:FIF,
author = "D. Feyel and A. {de La Pradelle}",
title = "The {FBM} {It{\^o}}'s Formula Through Analytic
Continuation",
journal = j-ELECTRON-J-PROBAB,
volume = "6",
pages = "26:1--26:22",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v6-99",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/99",
abstract = "The Fractional Brownian Motion can be extended to
complex values of the parameter $ \alpha $ for $ \Re
\alpha > {1 \over 2} $. This is a useful tool. Indeed,
the obtained process depends holomorphically on the
parameter, so that many formulas, as It{\^o} formula,
can be extended by analytic continuation. For large
values of $ \Re \alpha $, the stochastic calculus
reduces to a deterministic one, so that formulas are
very easy to prove. Hence they hold by analytic
continuation for $ \Re \alpha \leq 1 $, containing the
classical case $ \alpha = 1 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Wiener space, Sobolev space, Stochastic integral,
Fractional Brownian Motion, It{\^o}'s formula",
}
@Article{Jacka:2001:ECN,
author = "Saul Jacka and Jon Warren",
title = "Examples of Convergence and Non-convergence of
{Markov} Chains Conditioned Not To Die",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "1:1--1:22",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-100",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/100",
abstract = "In this paper we give two examples of evanescent
Markov chains which exhibit unusual behaviour on
conditioning to survive for large times. In the first
example we show that the conditioned processes converge
vaguely in the discrete topology to a limit with a
finite lifetime, but converge weakly in the Martin
topology to a non-Markovian limit. In the second
example, although the family of conditioned laws are
tight in the Martin topology, they possess multiple
limit points so that weak convergence fails
altogether.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Conditioned Markov process, evanescent process, Martin
boundary, Martin topology, superharmonic function,
Choquet representation, star, Kolmogorov K2 chain",
}
@Article{Lawler:2001:OAE,
author = "Gregory Lawler and Oded Schramm and Wendelin Werner",
title = "One-Arm Exponent for Critical {$2$D} Percolation",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "2:1--2:13",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-101",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/101",
abstract = "The probability that the cluster of the origin in
critical site percolation on the triangular grid has
diameter larger than $R$ is proved to decay like $R$ to
the power $ 5 / 48$ as $R$ goes to infinity.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Percolation, critical exponents",
}
@Article{Darling:2001:ILP,
author = "R. Darling",
title = "Intrinsic Location Parameter of a Diffusion Process",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "3:1--3:23",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-102",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/102",
abstract = "For nonlinear functions $f$ of a random vector $Y$, $
E[f(Y)]$ and $ f(E[Y])$ usually differ. Consequently
the mathematical expectation of $Y$ is not intrinsic:
when we change coordinate systems, it is not invariant.
This article is about a fundamental and hitherto
neglected property of random vectors of the form $ Y =
f(X(t))$, where $ X(t)$ is the value at time $t$ of a
diffusion process $X$: namely that there exists a
measure of location, called the ``intrinsic location
parameter'' (ILP), which coincides with mathematical
expectation only in special cases, and which is
invariant under change of coordinate systems. The
construction uses martingales with respect to the
intrinsic geometry of diffusion processes, and the heat
flow of harmonic mappings. We compute formulas which
could be useful to statisticians, engineers, and others
who use diffusion process models; these have immediate
application, discussed in a separate article, to the
construction of an intrinsic nonlinear analog to the
Kalman Filter. We present here a numerical simulation
of a nonlinear SDE, showing how well the ILP formula
tracks the mean of the SDE for a Euclidean geometry.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "intrinsic location parameter, gamma-martingale,
stochastic differential equation, forward--backwards
SDE, harmonic map, nonlinear heat equation",
}
@Article{Najim:2001:CTT,
author = "Jamal Najim",
title = "A {Cram{\'e}r} Type Theorem for Weighted Random
Variables",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "4:1--4:32",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-103",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/103",
abstract = "A Large Deviation Principle (LDP) is proved for the
family $ (1 / n) \sum_1^n f(x_i^n) Z_i $ where $ (1 /
n) \sum_1^n \delta_{x_i^n} $ converges weakly to a
probability measure on $R$ and $ (Z_i)_{i \in N}$ are $
R^d$-valued independent and identically distributed
random variables having some exponential moments,
i.e.,\par
$$ E e^{a |Z|} < \infty $$
for some $ 0 < a < \infty $. The main improvement of
this work is the relaxation of the steepness assumption
concerning the cumulant generating function of the
variables $ (Z_i)_{i \in N}$. In fact,
G{\"a}rtner-Ellis' theorem is no longer available in
this situation. As an application, we derive a LDP for
the family of empirical measures $ (1 / n) \sum_1^n Z_i
\delta_{x_i^n}$. These measures are of interest in
estimation theory (see Gamboa et al., Csiszar et al.),
gas theory (see Ellis et al., van den Berg et al.),
etc. We also derive LDPs for empirical processes in the
spirit of Mogul'skii's theorem. Various examples
illustrate the scope of our results.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Large Deviations, empirical means, empirical measures,
maximum entropy on the means",
}
@Article{Konig:2001:NCR,
author = "Wolfgang K{\"o}nig and Neil O'Connell and
S{\'e}bastien Roch",
title = "Non-Colliding Random Walks, Tandem Queues, and
Discrete Orthogonal Polynomial Ensembles",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "5:1--5:24",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-104",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/104",
abstract = "We show that the function $ h(x) = \prod_{i < j}(x_j -
x_i) $ is harmonic for any random walk in $ R^k $ with
exchangeable increments, provided the required moments
exist. For the subclass of random walks which can only
exit the Weyl chamber $ W = \{ x \colon x_1 < x_2 <
\cdots < x_k \} $ onto a point where $h$ vanishes, we
define the corresponding Doob $h$-transform. For
certain special cases, we show that the marginal
distribution of the conditioned process at a fixed time
is given by a familiar discrete orthogonal polynomial
ensemble. These include the Krawtchouk and Charlier
ensembles, where the underlying walks are binomial and
Poisson, respectively. We refer to the corresponding
conditioned processes in these cases as the Krawtchouk
and Charlier processes. In [O'Connell and Yor (2001b)],
a representation was obtained for the Charlier process
by considering a sequence of $ M / M / 1$ queues in
tandem. We present the analogue of this representation
theorem for the Krawtchouk process, by considering a
sequence of discrete-time $ M / M / 1$ queues in
tandem. We also present related results for random
walks on the circle, and relate a system of
non-colliding walks in this case to the discrete
analogue of the circular unitary ensemble (CUE).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Non-colliding random walks, tandem queues",
}
@Article{Zahle:2001:RBR,
author = "Iljana Z{\"a}hle",
title = "Renormalizations of Branching Random Walks in
Equilibrium",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "7:1--7:57",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-106",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/106",
abstract = "We study the $d$-dimensional branching random walk for
$ d > 2$. This process has extremal equilibria for
every intensity. We are interested in the large space
scale and large space-time scale behavior of the
equilibrium state. We show that the fluctuations of
space and space-time averages with a non-classical
scaling are Gaussian in the limit. For this purpose we
use the historical process, which allows a family
decomposition. To control the distribution of the
families we use the concept of canonical measures and
Palm distributions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Renormalization, branching random walk, Green's
function of random walks, Palm distribution",
}
@Article{Luo:2001:STP,
author = "S. Luo and John Walsh",
title = "A Stochastic Two-Point Boundary Value Problem",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "12:1--12:32",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-111",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/111",
abstract = "We investigate the two-point stochastic boundary-value
problem on $ [0, 1] $: \begin{equation}\label{1}
\begin{split} U'' &= f(U)\dot W + g(U, U')\\ U(0) &=
\xi\\ U(1)&= \eta. \end{split} \tag{1} \end{equation}
where $ \dot W $ is a white noise on $ [0, 1] $, $ \xi
$ and $ \eta $ are random variables, and $f$ and $g$
are continuous real-valued functions. This is the
stochastic analogue of the deterministic two point
boundary-value problem, which is a classical example of
bifurcation. We find that if $f$ and $g$ are affine,
there is no bifurcation: for any r.v. $ \xi $ and $
\eta $, (1) has a unique solution a.s. However, as soon
as $f$ is non-linear, bifurcation appears. We
investigate the question of when there is either no
solution whatsoever, a unique solution, or multiple
solutions. We give examples to show that all these
possibilities can arise. While our results involve
conditions on $f$ and $g$, we conjecture that the only
case in which there is no bifurcation is when $f$ is
affine.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic boundary-value problems, bifurcations",
}
@Article{Diaconis:2002:RWT,
author = "Persi Diaconis and Susan Holmes",
title = "Random Walks on Trees and Matchings",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "6:1--6:17",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-105",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/105",
abstract = "We give sharp rates of convergence for a natural
Markov chain on the space of phylogenetic trees and
dually for the natural random walk on the set of
perfect matchings in the complete graph on $ 2 n $
vertices. Roughly, the results show that $ (1 / 2) n
\log n $ steps are necessary and suffice to achieve
randomness. The proof depends on the representation
theory of the symmetric group and a bijection between
trees and matchings.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Markov Chain, Matchings, Phylogenetic Tree, Fourier
analysis, Zonal polynomials,
Coagulation-Fragmentation",
}
@Article{Mayer-Wolf:2002:ACC,
author = "Eddy Mayer-Wolf and Ofer Zeitouni and Martin Zerner",
title = "Asymptotics of Certain Coagulation--Fragmentation
Processes and Invariant {Poisson--Dirichlet} Measures",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "8:1--8:25",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-107",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/107",
abstract = "We consider Markov chains on the space of (countable)
partitions of the interval $ [0, 1] $, obtained first
by size biased sampling twice (allowing repetitions)
and then merging the parts with probability $ \beta_m $
(if the sampled parts are distinct) or splitting the
part with probability $ \beta_s $, according to a law $
\sigma $ (if the same part was sampled twice). We
characterize invariant probability measures for such
chains. In particular, if $ \sigma $ is the uniform
measure, then the Poisson--Dirichlet law is an
invariant probability measure, and it is unique within
a suitably defined class of ``analytic'' invariant
measures. We also derive transience and recurrence
criteria for these chains.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Partitions, coagulation, fragmentation, invariant
measures, Poisson--Dirichlet",
}
@Article{Evans:2002:ERW,
author = "Steven Evans",
title = "Eigenvalues of Random Wreath Products",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "9:1--9:15",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-108",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/108",
abstract = "Consider a uniformly chosen element $ X_n $ of the
$n$-fold wreath product $ \Gamma_n = G \wr G \wr \cdots
\wr G$, where $G$ is a finite permutation group acting
transitively on some set of size $s$. The eigenvalues
of $ X_n$ in the natural $ s^n$-dimensional permutation
representation (the composition representation) are
investigated by considering the random measure $ \Xi_n$
on the unit circle that assigns mass $1$ to each
eigenvalue. It is shown that if $f$ is a trigonometric
polynomial, then $ \lim_{n \rightarrow \infty } P \{
\int f d \Xi_n \ne s^n \int f d \lambda \} = 0$, where
$ \lambda $ is normalised Lebesgue measure on the unit
circle. In particular, $ s^{-n} \Xi_n$ converges weakly
in probability to $ \lambda $ as $ n \rightarrow \infty
$. For a large class of test functions $f$ with
non-terminating Fourier expansions, it is shown that
there exists a constant $c$ and a non-zero random
variable $W$ (both depending on $f$) such that $ c^{-n}
\int f d \Xi_n$ converges in distribution as $ n
\rightarrow \infty $ to $W$. These results have
applications to Sylow $p$-groups of symmetric groups
and autmorphism groups of regular rooted trees.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "random permutation, random matrix, Haar measure,
regular tree, Sylow, branching process, multiplicative
function",
}
@Article{Mueller:2002:HPR,
author = "Carl Mueller and Roger Tribe",
title = "Hitting Properties of a Random String",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "10:1--10:29",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-109",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/109",
abstract = "We consider Funaki's model of a random string taking
values in $ \mathbf {R}^d $. It is specified by the
following stochastic PDE,\par
$$ \frac {\partial u(x)}{\partial t} = \frac
{\partial^2 u(x)}{\partial x^2} + \dot {W}. $$
where $ \dot {W} = \dot {W}(x, t) $ is two-parameter
white noise, also taking values in $ \mathbf {R}^d $.
We find the dimensions in which the string hits points,
and in which it has double points of various types. We
also study the question of recurrence and transience.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Martingale, random set, strong martingale property",
}
@Article{Belitsky:2002:DSS,
author = "Vladimir Belitsky and Gunter Sch{\"u}tz",
title = "Diffusion and Scattering of Shocks in the Partially
Asymmetric Simple Exclusion Process",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "11:1--11:21",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-110",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/110",
abstract = "We study the behavior of shocks in the asymmetric
simple exclusion process on $Z$ whose initial
distribution is a product measure with a finite number
of shocks. We prove that if the particle hopping rates
of this process are in a particular relation with the
densities of the initial measure then the distribution
of this process at any time is a linear combination of
shock measures of the structure similar to that of the
initial distribution. The structure of this linear
combination allows us to interpret this result by
saying that the shocks of the initial distribution
perform continuous time random walks on $Z$ interacting
by the exclusion rule. We give explicit expressions for
the hopping rates of these random walks. The result is
derived with a help of quantum algebra technique. We
made the presentation self-contained for the benefit of
readers not acquainted with this approach, but
interested in applying it in the study of interacting
particle systems.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Asymmetric simple exclusion process, evolution of
shock measures, quantum algebra",
}
@Article{Winter:2002:MSA,
author = "Anita Winter",
title = "Multiple Scale Analysis of Spatial Branching Processes
under the Palm Distribution",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "13:1--13:74",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-112",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/112",
abstract = "We consider two types of measure-valued branching
processes on the lattice $ Z^d $. These are on the one
hand side a particle system, called branching random
walk, and on the other hand its continuous mass
analogue, a system of interacting diffusions also
called super random walk. It is known that the
long-term behavior differs sharply in low and high
dimensions: if $ d \leq 2 $ one gets local extinction,
while, for $ d \geq 3 $, the systems tend to a
non-trivial equilibrium. Due to Kallenberg's criterion,
local extinction goes along with clumping around a
'typical surviving particle.' This phenomenon is called
clustering. A detailed description of the clusters has
been given for the corresponding processes on $ R^2 $
in Klenke (1997). Klenke proved that with the right
scaling the mean number of particles over certain
blocks are asymptotically jointly distributed like
marginals of a system of coupled Feller diffusions,
called system of tree indexed Feller diffusions,
provided that the initial intensity is appropriately
increased to counteract the local extinction. The
present paper takes different remedy against the local
extinction allowing also for state-dependent branching
mechanisms. Instead of increasing the initial
intensity, the systems are described under the Palm
distribution. It will turn out together with the
results in Klenke (1997) that the change to the Palm
measure and the multiple scale analysis commute, as $ t
\to \infty $. The method of proof is based on the fact
that the tree indexed systems of the branching
processes and of the diffusions in the limit are
completely characterized by all their moments. We
develop a machinery to describe the space-time moments
of the superprocess effectively and explicitly.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "infinite particle system, superprocess, interacting
diffusion, clustering, Palm distribution, grove indexed
systems of diffusions, grove indexed systems of
branching models, Kallenberg's backward tree",
}
@Article{Matsumoto:2002:WFS,
author = "Hiroyuki Matsumoto and Setsuo Taniguchi",
title = "{Wiener} Functionals of Second Order and Their
{L{\'e}vy} Measures",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "14:1--14:30",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-113",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/113",
abstract = "The distributions of Wiener functionals of second
order are infinitely divisible. An explicit expression
of the associated L{\'e}vy measures in terms of the
eigenvalues of the corresponding Hilbert--Schmidt
operators on the Cameron--Martin subspace is presented.
In some special cases, a formula for the densities of
the distributions is given. As an application of the
explicit expression, an exponential decay property of
the characteristic functions of the Wiener functionals
is discussed. In three typical examples, complete
descriptions are given.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Wiener functional of second order, L{\'e}vy measure,
Mellin transform, exponential decay",
}
@Article{Dawson:2002:MCB,
author = "Donald Dawson and Alison Etheridge and Klaus
Fleischmann and Leonid Mytnik and Edwin Perkins and Jie
Xiong",
title = "Mutually Catalytic Branching in The Plane: Infinite
Measure States",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "15:1--15:61",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-114",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/114",
abstract = "A two-type infinite-measure-valued population in $ R^2
$ is constructed which undergoes diffusion and
branching. The system is interactive in that the
branching rate of each type is proportional to the
local density of the other type. For a collision rate
sufficiently small compared with the diffusion rate,
the model is constructed as a pair of
infinite-measure-valued processes which satisfy a
martingale problem involving the collision local time
of the solutions. The processes are shown to have
densities at fixed times which live on disjoint sets
and explode as they approach the interface of the two
populations. In the long-term limit (in law), local
extinction of one type is shown. Moreover the surviving
population is uniform with random intensity. The
process constructed is a rescaled limit of the
corresponding $ Z^2$-lattice model studied by Dawson
and Perkins (1998) and resolves the large scale
mass-time-space behavior of that model under critical
scaling. This part of a trilogy extends results from
the finite-measure-valued case, whereas uniqueness
questions are again deferred to the third part.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Catalyst, reactant, measure-valued branching,
interactive branching, state-dependent branching,
two-dimensional process, absolute continuity,
self-similarity, collision measure, collision local
time, martingale problem, moment equations, segregation
of ty",
}
@Article{Alves:2002:PTF,
author = "Oswaldo Alves and Fabio Machado and Serguei Popov",
title = "Phase Transition for the Frog Model",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "16:1--16:21",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-115",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/115",
abstract = "We study a system of simple random walks on graphs,
known as {\em frog model}. This model can be described
as follows: There are active and sleeping particles
living on some graph. Each active particle performs a
simple random walk with discrete time and at each
moment it may disappear with probability $ 1 - p $.
When an active particle hits a sleeping particle, the
latter becomes active. Phase transition results and
asymptotic values for critical parameters are presented
for $ Z^d $ and regular trees.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "simple random walk, critical probability,
percolation",
}
@Article{Abraham:2002:PSF,
author = "Romain Abraham and Laurent Serlet",
title = "{Poisson} Snake and Fragmentation",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "17:1--17:15",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-116",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/116",
abstract = "Our main object that we call the Poisson snake is a
Brownian snake as introduced by Le Gall. This process
has values which are trajectories of standard Poisson
process stopped at some random finite lifetime with
Brownian evolution. We use this Poisson snake to
construct a self-similar fragmentation as introduced by
Bertoin. A similar representation was given by Aldous
and Pitman using the Continuum Random Tree. Whereas
their proofs used approximation by discrete models, our
representation allows continuous time arguments.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Path-valued process, Brownian snake, Poisson process,
fragmentation, coalescence, self-similarity",
}
@Article{Lejay:2002:CSI,
author = "Antoine Lejay",
title = "On the Convergence of Stochastic Integrals Driven by
Processes Converging on account of a Homogenization
Property",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "18:1--18:18",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-117",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/117",
abstract = "We study the limit of functionals of stochastic
processes for which an homogenization result holds. All
these functionals involve stochastic integrals. Among
them, we consider more particularly the Levy area and
those giving the solutions of some SDEs. The main
question is to know whether or not the limit of the
stochastic integrals is equal to the stochastic
integral of the limit of each of its terms. In fact,
the answer may be negative, especially in presence of a
highly oscillating first-order differential term. This
provides us some counterexamples to the theory of good
sequence of semimartingales.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "stochastic differential equations, good sequence of
semimartingales, conditions UT and UCV, L{\'e}vy area",
}
@Article{Kolokoltsov:2002:TNE,
author = "Vassili Kolokoltsov and R. L. Schilling and A.
Tyukov",
title = "Transience and Non-explosion of Certain Stochastic
{Newtonian} Systems",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "19:1--19:19",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-118",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/118",
abstract = "We give sufficient conditions for non-explosion and
transience of the solution $ (x_t, p_t) $ (in
dimensions $ \geq 3$) to a stochastic Newtonian system
of the form\par
$$ \begin {cases} d x_t = p_t \, d t, \\ d p_t = -
\frac {\partial V(x_t) }{\partial x} \, d t - \frac {
\partial c(x_t) }{ \partial x} \, d \xi_t, \end {cases}
$$
where $ \{ \xi_t \}_{t \geq 0}$ is a $d$-dimensional
L{\'e}vy process, $ d \xi_t$ is an It{\^o} differential
and $ c \in C^2 (\mathbb {R}^d, \mathbb {R}^d)$, $ V
\in C^2 (\mathbb {R}^d, \mathbb {R})$ such that $ V
\geq 0$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "alpha-stable Levy processes; Levy processes;
Non-explosion.; Stochastic Newtonian systems;
Transience",
}
@Article{Fannjiang:2002:DLR,
author = "Albert Fannjiang and Tomasz Komorowski",
title = "Diffusion in Long-Range Correlated
{Ornstein--Uhlenbeck} Flows",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "20:1--20:22",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-119",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/119",
abstract = "We study a diffusion process with a molecular
diffusion and random Markovian--Gaussian drift for
which the usual (spatial) Peclet number is infinite. We
introduce a temporal Peclet number and we prove that,
under the finiteness of the temporal Peclet number, the
laws of diffusions under the diffusive rescaling
converge weakly, to the law of a Brownian motion. We
also show that the effective diffusivity has a finite,
nonzero limit as the molecular diffusion tends to
zero.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Ornstein--Uhlenbeck flow, martingale central limit
theorem, homogenization, Peclet number",
}
@Article{Warren:2002:NMP,
author = "Jon Warren",
title = "The Noise Made by a {Poisson} Snake",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "21:1--21:21",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-120",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/120",
abstract = "The purpose of this article is to study a coalescing
flow of sticky Brownian motions. Sticky Brownian motion
arises as a weak solution of a stochastic differential
equation, and the study of the flow reveals the nature
of the extra randomness that must be added to the
driving Brownian motion. This can be represented in
terms of Poissonian marking of the trees associated
with the excursions of Brownian motion. We also study
the noise, in the sense of Tsirelson, generated by the
flow. It is shown that this noise is not generated by
any Brownian motion, even though it is predictable.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "stochastic flow, sticky Brownian motion, coalescence,
stochastic differential equation, noise",
}
@Article{Atar:2002:SPC,
author = "Rami Atar and Amarjit Budhiraja",
title = "Stability Properties of Constrained Jump-Diffusion
Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "22:1--22:31",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-121",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/121",
abstract = "We consider a class of jump-diffusion processes,
constrained to a polyhedral cone $ G \subset \mathbb
{R}^n $, where the constraint vector field is constant
on each face of the boundary. The constraining
mechanism corrects for ``attempts'' of the process to
jump outside the domain. Under Lipschitz continuity of
the Skorohod map $ \Gamma $, it is known that there is
a cone $ {\cal C} $ such that the image $ \Gamma \phi $
of a deterministic linear trajectory $ \phi $ remains
bounded if and only if $ \dot \phi \in {\cal C} $.
Denoting the generator of a corresponding unconstrained
jump-diffusion by $ \cal L $, we show that a key
condition for the process to admit an invariant
probability measure is that for $ x \in G $, $ {\cal L}
\, {\rm id}(x) $ belongs to a compact subset of $ {\cal
C}^o $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Jump diffusion processes. The Skorohod map. Stability
cone. Harris recurrence",
}
@Article{Faure:2002:SNL,
author = "Mathieu Faure",
title = "Self-normalized Large Deviations for {Markov} Chains",
journal = j-ELECTRON-J-PROBAB,
volume = "7",
pages = "23:1--23:31",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v7-122",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/122",
abstract = "We prove a self-normalized large deviation principle
for sums of Banach space valued functions of a Markov
chain. Self-normalization applies to situations for
which a full large deviation principle is not
available. We follow the lead of Dembo and Shao
[DemSha98b] who state partial large deviations
principles for independent and identically distributed
random sequences.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Large deviations, Markov chains, partial large
deviation principles, self-normalization",
}
@Article{Dalang:2003:SNL,
author = "Robert Dalang and Carl Mueller",
title = "Some Non-Linear {S.P.D.E}'s That Are Second Order In
Time",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "1:1--1:21",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-123",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/123",
abstract = "We extend J. B. Walsh's theory of martingale measures
in order to deal with stochastic partial differential
equations that are second order in time, such as the
wave equation and the beam equation, and driven by
spatially homogeneous Gaussian noise. For such
equations, the fundamental solution can be a
distribution in the sense of Schwartz, which appears as
an integrand in the reformulation of the s.p.d.e. as a
stochastic integral equation. Our approach provides an
alternative to the Hilbert space integrals of
Hilbert--Schmidt operators. We give several examples,
including the beam equation and the wave equation, with
nonlinear multiplicative noise terms.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic wave equation, stochastic beam equation,
spatially homogeneous Gaussian noise, stochastic
partial differential equations",
}
@Article{Hamadene:2003:RBS,
author = "Said Hamad{\`e}ne and Youssef Ouknine",
title = "Reflected Backward Stochastic Differential Equation
with Jumps and Random Obstacle",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "2:1--2:20",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-124",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/124",
abstract = "In this paper we give a solution for the
one-dimensional reflected backward stochastic
differential equation when the noise is driven by a
Brownian motion and an independent Poisson point
process. We prove existence and uniqueness of the
solution in using penalization and the Snell envelope
theory. However both methods use a contraction in order
to establish the result in the general case. Finally,
we highlight the connection of such reflected BSDEs
with integro-differential mixed stochastic optimal
control.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Backward stochastic differential equation,
penalization, Poisson point process, martingale
representation theorem, integral-differential mixed
control",
}
@Article{Cheridito:2003:FOU,
author = "Patrick Cheridito and Hideyuki Kawaguchi and Makoto
Maejima",
title = "Fractional {Ornstein--Uhlenbeck} processes",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "3:1--3:14",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-125",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/125",
abstract = "The classical stationary Ornstein--Uhlenbeck process
can be obtained in two different ways. On the one hand,
it is a stationary solution of the Langevin equation
with Brownian motion noise. On the other hand, it can
be obtained from Brownian motion by the so called
Lamperti transformation. We show that the Langevin
equation with fractional Brownian motion noise also has
a stationary solution and that the decay of its
auto-covariance function is like that of a power
function. Contrary to that, the stationary process
obtained from fractional Brownian motion by the
Lamperti transformation has an auto-covariance function
that decays exponentially.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Fractional Brownian motion, Langevin equation,
Long-range dependence, Self-similar processes, Lamperti
transformation",
}
@Article{Dawson:2003:SDM,
author = "Donald Dawson and Andreas Greven",
title = "State Dependent Multitype Spatial Branching Processes
and their Longtime Behavior",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "4:1--4:93",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-126",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/126",
abstract = "The paper focuses on spatial multitype branching
systems with spatial components (colonies) indexed by a
countable group, for example $ Z^d $ or the
hierarchical group. As type space we allow continua and
describe populations in one colony as measures on the
type space. The spatial components of the system
interact via migration. Instead of the classical
independence assumption on the evolution of different
families of the branching population, we introduce
interaction between the families through a state
dependent branching rate of individuals and in addition
state dependent mean offspring of individuals. However
for most results we consider the critical case in this
work. The systems considered arise as diffusion limits
of critical multiple type branching random walks on a
countable group with interaction between individual
families induced by a branching rate and offspring mean
for a single particle, which depends on the total
population at the site at which the particle in
question is located.\par
The main purpose of this paper is to construct the
measure valued diffusions in question, characterize
them via well-posed martingale problems and finally
determine their longtime behavior, which includes some
new features. Furthermore we determine the dynamics of
two functionals of the system, namely the process of
total masses at the sites and the relative weights of
the different types in the colonies as system of
interacting diffusions respectively time-inhomogeneous
Fleming--Viot processes. This requires a detailed
analysis of path properties of the total mass
processes.\par
In addition to the above mentioned systems of
interacting measure valued processes we construct the
corresponding historical processes via well-posed
martingale problems. Historical processes include
information on the family structure, that is, the
varying degrees of relationship between
individuals.\par
Ergodic theorems are proved in the critical case for
both the process and the historical process as well as
the corresponding total mass and relative weights
functionals. The longtime behavior differs
qualitatively in the cases in which the symmetrized
motion is recurrent respectively transient. We see
local extinction in one case and honest equilibria in
the other.\par
This whole program requires the development of some new
techniques, which should be of interest in a wider
context. Such tools are dual processes in randomly
fluctuating medium with singularities and coupling for
systems with multi-dimensional components.\par
The results above are the basis for the analysis of the
large space-time scale behavior of such branching
systems with interaction carried out in a forthcoming
paper. In particular we study there the universality
properties of the longtime behavior and of the family
(or genealogical) structure, when viewed on large space
and time scales.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Spatial branching processes with interaction,
multitype branching processes with type-interaction,
historical process, universality, coupling of
multidimensional processes, coalescing random walks in
singular random environment",
}
@Article{Kesten:2003:BRW,
author = "Harry Kesten and Vladas Sidoravicius",
title = "Branching Random Walk with Catalysts",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "5:1--5:51",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-127",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/127",
abstract = "Shnerb et al. (2000), (2001) studied the following
system of interacting particles on $ \mathbb {Z}^d $:
There are two kinds of particles, called $A$-particles
and $B$-particles. The $A$-particles perform continuous
time simple random walks, independently of each other.
The jump rate of each $A$-particle is $ D_A$. The
$B$-particles perform continuous time simple random
walks with jump rate $ D_B$, but in addition they die
at rate $ \delta $ and a $B$-particle at $x$ at time
$s$ splits into two particles at $x$ during the next $
d s$ time units with a probability $ \beta N_A(x, s)d s
+ o(d s)$, where $ N_A(x, s) \; (N_B(x, s))$ denotes
the number of $A$-particles (respectively
$B$-particles) at $x$ at time $s$. Conditionally on the
$A$-system, the jumps, deaths and splittings of
different $B$-particles are independent. Thus the
$B$-particles perform a branching random walk, but with
a birth rate of new particles which is proportional to
the number of $A$-particles which coincide with the
appropriate $B$-particles. One starts the process with
all the $ N_A(x, 0), \, x \in \mathbb {Z}^d$, as
independent Poisson variables with mean $ \mu_A$, and
the $ N_B(x, 0), \, x \in \mathbb {Z}^d$, independent
of the $A$-system, translation invariant and with mean
$ \mu_B$.\par
Shnerb et al. (2000) made the interesting discovery
that in dimension 1 and 2 the expectation $ \mathbb {E}
\{ N_B(x, t) \} $ tends to infinity, {\em no matter
what the values of } $ \delta, \beta, D_A$, $ D_B,
\mu_A, \mu_B \in (0, \infty)$ {\em are}. We shall show
here that nevertheless {\em there is a phase transition
in all dimensions}, that is, the system becomes
(locally) extinct for large $ \delta $ but it survives
for $ \beta $ large and $ \delta $ small.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Branching random walk, survival, extinction",
}
@Article{Sturm:2003:CPP,
author = "Anja Sturm",
title = "On Convergence of Population Processes in Random
Environments to the Stochastic Heat Equation with
Colored Noise",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "6:1--6:39",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-129",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/129",
abstract = "We consider the stochastic heat equation with a
multiplicative colored noise term on the real space for
dimensions greater or equal to 1. First, we prove
convergence of a branching particle system in a random
environment to this stochastic heat equation with
linear noise coefficients. For this stochastic partial
differential equation with more general non-Lipschitz
noise coefficients we show convergence of associated
lattice systems, which are infinite dimensional
stochastic differential equations with correlated noise
terms, provided that uniqueness of the limit is known.
In the course of the proof, we establish existence and
uniqueness of solutions to the lattice systems, as well
as a new existence result for solutions to the
stochastic heat equation. The latter are shown to be
jointly continuous in time and space under some mild
additional assumptions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Heat equation, colored noise, stochastic partial
differential equation, superprocess, weak convergence,
particle representation, random environment, existence
theorem",
}
@Article{Bottcher:2003:NPL,
author = "Albrecht B{\"o}ttcher and Sergei Grudsky",
title = "The Norm of the Product of a Large Matrix and a Random
Vector",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "7:1--7:29",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-132",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/132",
abstract = "Given a real or complex $ n \times n $ matrix $ A_n $,
we compute the expected value and the variance of the
random variable $ \| A_n x \|^2 / \| A_n \|^2 $, where
$x$ is uniformly distributed on the unit sphere of $
R^n$ or $ C^n$. The result is applied to several
classes of structured matrices. It is in particular
shown that if $ A_n$ is a Toeplitz matrix $ T_n(b)$,
then for large $n$ the values of $ \| A_n x \| / \| A_n
\| $ cluster fairly sharply around $ \| b \|_2 / \| b
\|_\infty $ if $b$ is bounded and around zero in case
$b$ is unbounded.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Condition number. Matrix norm. Random vector. Toeplitz
matrix",
}
@Article{Fleischmann:2003:CSS,
author = "Klaus Fleischmann and Leonid Mytnik",
title = "Competing Species Superprocesses with Infinite
Variance",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "8:1--8:59",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-136",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/136",
abstract = "We study pairs of interacting measure-valued branching
processes (superprocesses) with alpha-stable migration
and $ (1 + \beta)$-branching mechanism. The interaction
is realized via some killing procedure. The collision
local time for such processes is constructed as a limit
of approximating collision local times. For certain
dimensions this convergence holds uniformly over all
pairs of such interacting superprocesses. We use this
uniformity to prove existence of a solution to a
competing species martingale problem under a natural
dimension restriction. The competing species model
describes the evolution of two populations where
individuals of different types may kill each other if
they collide. In the case of Brownian migration and
finite variance branching, the model was introduced by
Evans and Perkins (1994). The fact that now the
branching mechanism does not have finite variance
requires the development of new methods for handling
the collision local time which we believe are of some
independent interest.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Superprocess with killing, competing superprocesses,
interactive superprocesses, superprocess with
immigration, measure-valued branching, interactive
branching, state-dependent branching, collision
measure, collision local time, martingale problem",
}
@Article{Bai:2003:BEB,
author = "Zhi-Dong Bai and Hsien-Kuei Hwang and Tsung-Hsi
Tsai",
title = "{Berry--Ess{\'e}en} Bounds for the Number of Maxima in
Planar Regions",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "9:1--9:26",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-137",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/137",
abstract = "We derive the optimal convergence rate $ O(n^{-1 / 4})
$ in the central limit theorem for the number of maxima
in random samples chosen uniformly at random from the
right equilateral triangle with two sides parallel to
the axes, the hypotenuse with the slope $ - 1 $ and
constituting the top part of the boundary of the
triangle. A local limit theorem with rate is also
derived. The result is then applied to the number of
maxima in general planar regions (upper-bounded by some
smooth decreasing curves) for which a near-optimal
convergence rate to the normal distribution is
established.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Dominance, Maximal points, Central limit theorem,
{Berry--Ess{\'e}en} bound, Local limit theorem, Method
of moments",
}
@Article{Fitzsimmons:2003:HRM,
author = "Patrick Fitzsimmons and Ronald Getoor",
title = "Homogeneous Random Measures and Strongly Supermedian
Kernels of a {Markov} Process",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "10:1--10:54",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-142",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/142",
abstract = "The potential kernel of a positive {\em left} additive
functional (of a strong Markov process $X$) maps
positive functions to {\em strongly supermedian}
functions and satisfies a variant of the classical {\em
domination principle} of potential theory. Such a
kernel $V$ is called a {\em regular strongly
supermedian } kernel in recent work of L. Beznea and N.
Boboc. We establish the converse: Every regular
strongly supermedian kernel $V$ is the potential kernel
of a random measure homogeneous on $ [0, \infty [$.
Under additional finiteness conditions such random
measures give rise to left additive functionals. We
investigate such random measures, their potential
kernels, and their associated characteristic measures.
Given a left additive functional $A$ (not necessarily
continuous), we give an explicit construction of a
simple Markov process $Z$ whose resolvent has initial
kernel equal to the potential kernel $ U_{\! A}$. The
theory we develop is the probabilistic counterpart of
the work of Beznea and Boboc. Our main tool is the
Kuznetsov process associated with $X$ and a given
excessive measure $m$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Homogeneous random measure, additive functional,
Kuznetsov measure, potential kernel, characteristic
measure, strongly supermedian, smooth measure",
}
@Article{Zhou:2003:CBC,
author = "Xiaowen Zhou",
title = "Clustering Behavior of a Continuous-Sites
Stepping-Stone Model with {Brownian} Migration",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "11:1--11:15",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-141",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/141",
abstract = "Clustering behavior is studied for a continuous-sites
stepping-stone model with Brownian migration. It is
shown that, if the model starts with the same mixture
of different types of individuals over each site, then
it will evolve in a way such that the site space is
divided into disjoint intervals where only one type of
individuals appear in each interval. Those intervals
(clusters) are growing as time $t$ goes to infinity.
The average size of the clusters at a fixed time $t$ is
of the order of square root of $t$. Clusters at
different times or sites are asymptotically independent
as the difference of either the times or the sites goes
to infinity.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "clustering; coalescing Brownian motion; stepping-stone
model",
}
@Article{Marquez-Carreras:2003:LDP,
author = "David Marquez-Carreras and Monica Sarra",
title = "Large Deviation Principle for a Stochastic Heat
Equation With Spatially Correlated Noise",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "12:1--12:39",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-146",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/146",
abstract = "In this paper we prove a large deviation principle
(LDP) for a perturbed stochastic heat equation defined
on $ [0, T] \times [0, 1]^d $. This equation is driven
by a Gaussian noise, white in time and correlated in
space. Firstly, we show the Holder continuity for the
solution of the stochastic heat equation. Secondly, we
check that our Gaussian process satisfies an LDP and
some requirements on the skeleton of the solution.
Finally, we prove the called Freidlin--Wentzell
inequality. In order to obtain all these results we
need precise estimates of the fundamental solution of
this equation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic partial differential equation, stochastic
heat equation, Gaussian noise, large deviation
principle",
}
@Article{Gao:2003:LTH,
author = "Fuchang Gao and Jan Hannig and Tzong-Yow Lee and Fred
Torcaso",
title = "{Laplace} Transforms via {Hadamard} Factorization",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "13:1--13:20",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-151",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/151",
abstract = "In this paper we consider the Laplace transforms of
some random series, in particular, the random series
derived as the squared $ L_2 $ norm of a Gaussian
stochastic process. Except for some special cases,
closed form expressions for Laplace transforms are, in
general, rarely obtained. It is the purpose of this
paper to show that for many Gaussian random processes
the Laplace transform can be expressed in terms of well
understood functions using complex-analytic theorems on
infinite products, in particular, the Hadamard
Factorization Theorem. Together with some tools from
linear differential operators, we show that in many
cases the Laplace transforms can be obtained with
little work. We demonstrate this on several examples.
Of course, once the Laplace transform is known
explicitly one can easily calculate the corresponding
exact $ L_2 $ small ball probabilities using Sytaja
Tauberian theorem. Some generalizations are
mentioned.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Small ball probability, Laplace Transforms, Hadamard's
factorization theorem",
}
@Article{Tudor:2003:IFL,
author = "Ciprian Tudor and Frederi Viens",
title = "{It{\^o}} Formula and Local Time for the Fractional
{Brownian} Sheet",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "14:1--14:31",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-155",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/155",
abstract = "Using the techniques of the stochastic calculus of
variations for Gaussian processes, we derive an It{\^o}
formula for the fractional Brownian sheet with Hurst
parameters bigger than $ 1 / 2 $. As an application, we
give a stochastic integral representation for the local
time of the fractional Brownian sheet.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "fractional Brownian sheet, It{\^o} formula, local
time, Tanaka formula, Malliavin calculus",
}
@Article{Dembo:2003:BMC,
author = "Amir Dembo and Yuval Peres and Jay Rosen",
title = "{Brownian} Motion on Compact Manifolds: Cover Time and
Late Points",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "15:1--15:14",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-139",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/139",
abstract = "Let $M$ be a smooth, compact, connected Riemannian
manifold of dimension $ d > 2$ and without boundary.
Denote by $ T(x, r)$ the hitting time of the ball of
radius $r$ centered at $x$ by Brownian motion on $M$.
Then, $ C_r(M) = \sup_{x \in M} T(x, r)$ is the time it
takes Brownian motion to come within $r$ of all points
in $M$. We prove that $ C_r(M) / (r^{2 - d}| \log r|)$
tends to $ \gamma_d V(M)$ almost surely as $ r \to 0$,
where $ V(M)$ is the Riemannian volume of $M$. We also
obtain the ``multi-fractal spectrum'' $ f(\alpha)$ for
``late points'', i.e., the dimension of the set of $
\alpha $-late points $x$ in $M$ for which $ \limsup_{r
\to 0} T(x, r) / (r^{2 - d}| \log r|) = \alpha > 0$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion, manifold, cover time, Wiener
sausage",
}
@Article{Budhiraja:2003:LDE,
author = "Amarjit Budhiraja and Paul Dupuis",
title = "Large Deviations for the Emprirical Measures of
Reflecting {Brownian} Motion and Related Constrained
Processes in {$ R_+ $}",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "16:1--16:46",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-154",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/154",
abstract = "We consider the large deviations properties of the
empirical measure for one dimensional constrained
processes, such as reflecting Brownian motion, the
M/M/1 queue, and discrete time analogues. Because these
processes do not satisfy the strong stability
assumptions that are usually assumed when studying the
empirical measure, there is significant probability
(from the perspective of large deviations) that the
empirical measure charges the point at infinity. We
prove the large deviation principle and identify the
rate function for the empirical measure for these
processes. No assumption of any kind is made with
regard to the stability of the underlying process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Markov process, constrained process, large deviations,
empirical measure, stability, reflecting Brownian
motion",
}
@Article{Delmas:2003:CML,
author = "Jean-Fran{\c{c}}ois Delmas",
title = "Computation of Moments for the Length of the
One-Dimensional {ISE} Support",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "17:1--17:15",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-161",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/161",
abstract = "We consider in this paper the support $ [L', R'] $ of
the one dimensional Integrated Super Brownian
Excursion. We determine the distribution of $ (R', L')
$ through a modified Laplace transform. Then we give an
explicit value for the first two moments of $ R' $ as
well as the covariance of $ R' $ and $ {L'} $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian snake; ISE",
}
@Article{Gradinaru:2003:AFS,
author = "Mihai Gradinaru and Ivan Nourdin",
title = "Approximation at First and Second Order of $m$-order
Integrals of the Fractional {Brownian} Motion and of
Certain Semimartingales",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "18:1--18:26",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-166",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/166",
abstract = "Let $X$ be the fractional Brownian motion of any Hurst
index $ H \in (0, 1)$ (resp. a semimartingale) and set
$ \alpha = H$ (resp. $ \alpha = \frac {1}{2}$). If $Y$
is a continuous process and if $m$ is a positive
integer, we study the existence of the limit, as $
\varepsilon \rightarrow 0$, of the approximations\par
$$ I_{\varepsilon }(Y, X) := \left \{ \int_0^t Y_s
\left (\frac {X_{s + \varepsilon } -
X_s}{\varepsilon^{\alpha }} \right)^m d s, \, t \geq 0
\right \} $$
of $m$-order integral of $Y$ with respect to $X$. For
these two choices of $X$, we prove that the limits are
almost sure, uniformly on each compact interval, and
are in terms of the $m$-th moment of the Gaussian
standard random variable. In particular, if $m$ is an
odd integer, the limit equals to zero. In this case,
the convergence in distribution, as $ \varepsilon
\rightarrow 0$, of $ \varepsilon^{- \frac {1}{2}}
I_{\varepsilon }(1, X)$ is studied. We prove that the
limit is a Brownian motion when $X$ is the fractional
Brownian motion of index $ H \in (0, \frac {1}{2}]$,
and it is in term of a two dimensional standard
Brownian motion when $X$ is a semimartingale.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Maejima:2003:LMS,
author = "Makoto Maejima and Kenji Yamamoto",
title = "Long-Memory Stable {Ornstein--Uhlenbeck} Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "19:1--19:18",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-168",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/168",
abstract = "The solution of the Langevin equation driven by a
L{\'e}vy process noise has been well studied, under the
name of Ornstein--Uhlenbeck type process. It is a
stationary Markov process. When the noise is fractional
Brownian motion, the covariance of the stationary
solution process has been studied by the first author
with different coauthors. In the present paper, we
consider the Langevin equation driven by a linear
fractional stable motion noise, which is a selfsimilar
process with long-range dependence but does not have
finite variance, and we investigate the dependence
structure of the solution process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Lachal:2003:DST,
author = "Aime Lachal",
title = "Distributions of Sojourn Time, Maximum and Minimum for
Pseudo-Processes Governed by Higher-Order Heat-Type
Equations",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "20:1--20:53",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-178",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/178",
abstract = "The higher-order heat-type equation $ \partial u /
\partial t = \pm \partial^n u / \partial x^n $ has been
investigated by many authors. With this equation is
associated a pseudo-process $ (X_t)_{t \ge 0} $ which
is governed by a signed measure. In the even-order
case, Krylov (1960) proved that the classical arc-sine
law of Paul Levy for standard Brownian motion holds for
the pseudo-process $ (X_t)_{t \ge 0} $, that is, if $
T_t $ is the sojourn time of $ (X_t)_{t \ge 0} $ in the
half line $ (0, + \infty) $ up to time $t$, then $
P(T_t \in d s) = \frac {ds}{\pi \sqrt {s(t - s)}}$, $ 0
< s < t$. Orsingher (1991) and next Hochberg and
Orsingher (1994) obtained a counterpart to that law in
the odd cases $ n = 3, 5, 7.$ Actually Hochberg and
Orsingher (1994) proposed a more or less explicit
expression for that new law in the odd-order general
case and conjectured a quite simple formula for it. The
distribution of $ T_t$ subject to some conditioning has
also been studied by Nikitin \& Orsingher (2000) in the
cases $ n = 3, 4.$ In this paper, we prove that the
conjecture of Hochberg and Orsingher (1994) is true and
we extend the results of Nikitin \& Orsingher for any
integer $n$. We also investigate the distributions of
maximal and minimal functionals of $ (X_t)_{t \ge 0}$,
as well as the distribution of the last time before
becoming definitively negative up to time $t$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Gao:2003:CTS,
author = "Fuchang Gao and Jan Hannig and Fred Torcaso",
title = "Comparison Theorems for Small Deviations of Random
Series",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "21:1--21:17",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-147",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/147",
abstract = "Let $ {\xi_n} $ be a sequence of i.i.d. positive
random variables with common distribution function $
F(x) $. Let $ {a_n} $ and $ {b_n} $ be two positive
non-increasing summable sequences such that $ {\prod_{n
= 1}^{\infty }(a_n / b_n)} $ converges. Under some mild
assumptions on $F$, we prove the following
comparison\par
$$ P \left (\sum_{n = 1}^{\infty }a_n \xi_n \leq
\varepsilon \right) \sim \left (\prod_{n = 1}^{\infty }
\frac {b_n}{a_n} \right)^{- \alpha } P \left (\sum_{n =
1}^{\infty }b_n \xi_n \leq \varepsilon \right), $$
where\par
$$ { \alpha = \lim_{x \to \infty } \frac {\log F(1 /
x)}{\log x}} < 0 $$
is the index of variation of $ F(1 / \cdot)$. When
applied to the case $ \xi_n = |Z_n|^p$, where $ Z_n$
are independent standard Gaussian random variables, it
affirms a conjecture of Li cite {Li1992a}.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "small deviation, random series, bounded variation",
}
@Article{Appleby:2003:EAS,
author = "John Appleby and Alan Freeman",
title = "Exponential Asymptotic Stability of Linear
{It{\^o}--Volterra} Equation with Damped Stochastic
Perturbations",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "22:1--22:22",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-179",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/179",
abstract = "This paper studies the convergence rate of solutions
of the linear It{\^o}-Volterra equation\par
$$ d X(t) = \left (A X(t) + \int_0^t K(t - s)X(s), d s
\right) \, d t + \Sigma (t) \, d W(t) \tag {1} $$
where $K$ and $ \Sigma $ are continuous matrix-valued
functions defined on $ \mathbb {R}^+$, and $ (W(t))_{t
\geq 0}$ is a finite-dimensional standard Brownian
motion. It is shown that when the entries of $K$ are
all of one sign on $ \mathbb {R}^+$, that (i) the
almost sure exponential convergence of the solution to
zero, (ii) the $p$-th mean exponential convergence of
the solution to zero (for all $ p > 0$), and (iii) the
exponential integrability of the entries of the kernel
$K$, the exponential square integrability of the
entries of noise term $ \Sigma $, and the uniform
asymptotic stability of the solutions of the
deterministic version of (1) are equivalent. The paper
extends a result of Murakami which relates to the
deterministic version of this problem.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Volkov:2003:ERW,
author = "Stanislav Volkov",
title = "Excited Random Walk on Trees",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "23:1--23:15",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-180",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/180",
abstract = "We consider a nearest-neighbor stochastic process on a
rooted tree $G$ which goes toward the root with
probability $ 1 - \varepsilon $ when it visits a vertex
for the first time. At all other times it behaves like
a simple random walk on $G$. We show that for all $
\varepsilon \ge 0$ this process is transient. Also we
consider a generalization of this process and establish
its transience in {\em some} cases.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Ocone:2004:DVC,
author = "Daniel Ocone and Ananda Weerasinghe",
title = "Degenerate Variance Control in the One-dimensional
Stationary Case",
journal = j-ELECTRON-J-PROBAB,
volume = "8",
pages = "24:27",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v8-181",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/181",
abstract = "We study the problem of stationary control by adaptive
choice of the diffusion coefficient in the case that
control degeneracy is allowed and the drift admits a
unique, asymptotically stable equilibrium point. We
characterize the optimal value and obtain it as an
Abelian limit of optimal discounted values and as a
limiting average of finite horizon optimal values, and
we also characterize the optimal stationary strategy.
In the case of linear drift, the optimal stationary
value is expressed in terms of the solution of an
optimal stopping problem. We generalize the above
results to allow unbounded cost functions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "stationary control, degenerate variance control;
stochastic control",
}
@Article{Kozma:2004:AED,
author = "Gady Kozma and Ehud Schreiber",
title = "An asymptotic expansion for the discrete harmonic
potential",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "1:1--1:17",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-170",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/170",
abstract = "We give two algorithms that allow to get arbitrary
precision asymptotics for the harmonic potential of a
random walk.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Barbour:2004:NUB,
author = "Andrew Barbour and Kwok Choi",
title = "A non-uniform bound for translated {Poisson}
approximation",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "2:18--2:36",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-182",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/182",
abstract = "Let $ X_1, \ldots, X_n $ be independent, integer
valued random variables, with $ p^{\text {th}} $
moments, $ p > 2 $, and let $W$ denote their sum. We
prove bounds analogous to the classical non-uniform
estimates of the error in the central limit theorem,
but now, for approximation of $ {\cal L}(W)$ by a
translated Poisson distribution. The advantage is that
the error bounds, which are often of order no worse
than in the classical case, measure the accuracy in
terms of total variation distance. In order to have
good approximation in this sense, it is necessary for $
{\cal L}(W)$ to be sufficiently smooth; this
requirement is incorporated into the bounds by way of a
parameter $ \alpha $, which measures the average
overlap between $ {\cal L}(X_i)$ and $ {\cal L}(X_i +
1), 1 \leq i \leq n$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "non-uniform bounds; Stein's method; total variation;
translated Poisson approximation",
}
@Article{Aldous:2004:BBA,
author = "David Aldous and Gregory Miermont and Jim Pitman",
title = "{Brownian} Bridge Asymptotics for Random
$p$-Mappings",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "3:37--3:56",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-186",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/186",
abstract = "The Joyal bijection between doubly-rooted trees and
mappings can be lifted to a transformation on function
space which takes tree-walks to mapping-walks. Applying
known results on weak convergence of random tree walks
to Brownian excursion, we give a conceptually simpler
rederivation of the Aldous--Pitman (1994) result on
convergence of uniform random mapping walks to
reflecting Brownian bridge, and extend this result to
random $p$-mappings.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian bridge, Brownian excursion, Joyal map, random
mapping, random tree, weak convergence",
}
@Article{Haas:2004:GSS,
author = "B{\'e}n{\'e}dicte Haas and Gr{\'e}gory Miermont",
title = "The Genealogy of Self-similar Fragmentations with
Negative Index as a Continuum Random Tree",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "4:57--4:97",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-187",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/187",
abstract = "We encode a certain class of stochastic fragmentation
processes, namely self-similar fragmentation processes
with a negative index of self-similarity, into a metric
family tree which belongs to the family of Continuum
Random Trees of Aldous. When the splitting times of the
fragmentation are dense near 0, the tree can in turn be
encoded into a continuous height function, just as the
Brownian Continuum Random Tree is encoded in a
normalized Brownian excursion. Under mild hypotheses,
we then compute the Hausdorff dimensions of these
trees, and the maximal H{\"o}lder exponents of the
height functions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Mueller:2004:SPA,
author = "Carl Mueller and Roger Tribe",
title = "A Singular Parabolic {Anderson} Model",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "5:98--5:144",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-189",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/189",
abstract = "We consider the heat equation with a singular random
potential term. The potential is Gaussian with mean 0
and covariance given by a small constant times the
inverse square of the distance. Solutions exist as
singular measures, under suitable assumptions on the
initial conditions and for sufficiently small noise. We
investigate various properties of the solutions using
such tools as scaling, self-duality and moment
formulae. This model lies on the boundary between
nonexistence and smooth solutions. It gives a new
model, other than the superprocess, which has
measure-valued solutions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "stochastic partial differential equations",
}
@Article{Fernandez:2004:CCC,
author = "Roberto Fernandez and Gregory Maillard",
title = "Chains with Complete Connections and One-Dimensional
{Gibbs} Measures",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "6:145--6:176",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-149",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/149",
abstract = "We discuss the relationship between one-dimensional
Gibbs measures and discrete-time processes (chains). We
consider finite-alphabet (finite-spin) systems,
possibly with a grammar (exclusion rule). We establish
conditions for a stochastic process to define a Gibbs
measure and vice versa. Our conditions generalize well
known equivalence results between ergodic Markov chains
and fields, as well as the known Gibbsian character of
processes with exponential continuity rate. Our
arguments are purely probabilistic; they are based on
the study of regular systems of conditional
probabilities (specifications). Furthermore, we discuss
the equivalence of uniqueness criteria for chains and
fields and we establish bounds for the continuity rates
of the respective systems of finite-volume conditional
probabilities. As an auxiliary result we prove a
(re)construction theorem for specifications starting
from single-site conditioning, which applies in a more
general setting (general spin space, specifications not
necessarily Gibbsian).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Discrete-time processes, Chains with complete
connections, Gibbs measures, Markov chains",
}
@Article{Ledoux:2004:DOS,
author = "Michel Ledoux",
title = "Differential Operators and Spectral Distributions of
Invariant Ensembles from the Classical Orthogonal
Polynomials. {The} Continuous Case",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "7:177--7:208",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-191",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/191",
abstract = "Following the investigation by U. Haagerup and S.
Thorbjornsen, we present a simple differential approach
to the limit theorems for empirical spectral
distributions of complex random matrices from the
Gaussian, Laguerre and Jacobi Unitary Ensembles. In the
framework of abstract Markov diffusion operators, we
derive by the integration by parts formula differential
equations for Laplace transforms and recurrence
equations for moments of eigenfunction measures. In
particular, a new description of the equilibrium
measures as adapted mixtures of the universal arcsine
law with an independent uniform distribution is
emphasized. The moment recurrence relations are used to
describe sharp, non asymptotic, small deviation
inequalities on the largest eigenvalues at the rate
given by the Tracy--Widom asymptotics.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Doney:2004:STB,
author = "Ronald Doney",
title = "Small-time Behaviour of {L{\'e}vy} Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "8:209--8:229",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-193",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/193",
abstract = "In this paper a neccessary and sufficient condition is
established for the probability that a L{\'e}vy process
is positive at time $t$ to tend to 1 as $t$ tends to 0.
This condition is expressed in terms of the
characteristics of the process, and is also shown to be
equivalent to two probabilistic statements about the
behaviour of the process for small time $t$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Alabert:2004:SDE,
author = "Aureli Alabert and Miguel Angel Marmolejo",
title = "Stochastic differential equations with boundary
conditions driven by a {Poisson} noise",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "9:230--254",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-157",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/157",
abstract = "We consider one-dimensional stochastic differential
equations with a boundary condition, driven by a
Poisson process. We study existence and uniqueness of
solutions and the absolute continuity of the law of the
solution. In the case when the coefficients are linear,
we give an explicit form of the solution and study the
reciprocal process property.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "boundary conditions; Poisson noise; reciprocal
processes; stochastic differential equations",
}
@Article{Garet:2004:PTS,
author = "Olivier Garet",
title = "Percolation Transition for Some Excursion Sets",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "10:255--10:292",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-196",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/196",
abstract = "We consider a random field $ (X_n)_{n \in \mathbb
{Z}^d} $ and investigate when the set $ A_h = \{ k \in
\mathbb {Z}^d; \vert X_k \vert \ge h \} $ has infinite
clusters. The main problem is to decide whether the
critical level\par
$$ h_c = \sup \{ h \in R \colon P(A_h \text { has an
infinite cluster }) > 0 \} $$
is neither $0$ nor $ + \infty $. Thus, we say that a
percolation transition occurs. In a first time, we show
that weakly dependent Gaussian fields satisfy to a
well-known criterion implying the percolation
transition. Then, we introduce a concept of percolation
along reasonable paths and therefore prove a phenomenon
of percolation transition for reasonable paths even for
strongly dependent Gaussian fields. This allows to
obtain some results of percolation transition for
oriented percolation. Finally, we study some Gibbs
states associated to a perturbation of a ferromagnetic
quadratic interaction. At first, we show that a
transition percolation occurs for superstable
potentials. Next, we go to the critical case and show
that a transition percolation occurs for directed
percolation when $ d \ge 4$. We also note that the
assumption of ferromagnetism can be relaxed when we
deal with Gaussian Gibbs measures, i.e., when there is
no perturbation of the quadratic interaction.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Kurkova:2004:ISC,
author = "Irina Kurkova and Serguei Popov and M. Vachkovskaia",
title = "On Infection Spreading and Competition between
Independent Random Walks",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "11:293--11:315",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-197",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/197",
abstract = "We study the models of competition and spreading of
infection for infinite systems of independent random
walks. For the competition model, we investigate the
question whether one of the spins prevails with
probability one. For the infection spreading, we give
sufficient conditions for recurrence and transience
(i.e., whether the origin will be visited by infected
particles infinitely often a.s.).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Dawson:2004:HEB,
author = "Donald Dawson and Luis Gorostiza and Anton
Wakolbinger",
title = "Hierarchical Equilibria of Branching Populations",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "12:316--12:381",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-200",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/200",
abstract = "The objective of this paper is the study of the
equilibrium behavior of a population on the
hierarchical group $ \Omega_N $ consisting of families
of individuals undergoing critical branching random
walk and in addition these families also develop
according to a critical branching process. Strong
transience of the random walk guarantees existence of
an equilibrium for this two-level branching system. In
the limit $ N \to \infty $ (called the {\em
hierarchical mean field limit}), the equilibrium
aggregated populations in a nested sequence of balls $
B^{(N)}_\ell $ of hierarchical radius $ \ell $ converge
to a backward Markov chain on $ \mathbb {R_+} $. This
limiting Markov chain can be explicitly represented in
terms of a cascade of subordinators which in turn makes
possible a description of the genealogy of the
population.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Multilevel branching, hierarchical mean-field limit,
strong transience, genealogy",
}
@Article{Kendall:2004:CIK,
author = "Wilfrid Kendall and Catherine Price",
title = "Coupling Iterated {Kolmogorov} Diffusions",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "13:382--13:410",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-201",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/201",
abstract = "The {\em Kolmogorov-1934 diffusion} is the
two-dimensional diffusion generated by real Brownian
motion and its time integral. In this paper we
construct successful co-adapted couplings for iterated
Kolmogorov diffusions defined by adding iterated time
integrals as further components to the original
Kolmogorov diffusion. A Laplace-transform argument
shows it is not possible successfully to couple all
iterated time integrals at once; however we give an
explicit construction of a successful co-adapted
coupling method for Brownian motion, its time integral,
and its twice-iterated time integral; and a more
implicit construction of a successful co-adapted
coupling method which works for finite sets of iterated
time integrals.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{vonRenesse:2004:ICR,
author = "Max-K. von Renesse",
title = "Intrinsic Coupling on {Riemannian} Manifolds and
Polyhedra",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "14:411--14:435",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-205",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/205",
abstract = "Starting from a central limit theorem for geometric
random walks we give an elementary construction of
couplings between Brownian motions on Riemannian
manifolds. This approach shows that cut locus phenomena
are indeed inessential for Kendall's and Cranston's
stochastic proof of gradient estimates for harmonic
functions on Riemannian manifolds with lower curvature
bounds. Moreover, since the method is based on an
asymptotic quadruple inequality and a central limit
theorem only it may be extended to certain non smooth
spaces which we illustrate by the example of Riemannian
polyhedra. Here we also recover the classical heat
kernel gradient estimate which is well known from the
smooth setting.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Central Limit Theorem; Coupling; Gradient Estimates",
}
@Article{Loewe:2004:RMR,
author = "Matthias Loewe and Heinrich Matzinger and Franz
Merkl",
title = "Reconstructing a Multicolor Random Scenery seen along
a Random Walk Path with Bounded Jumps",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "15:436--15:507",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-206",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/206",
abstract = "Kesten noticed that the scenery reconstruction method
proposed by Matzinger in his PhD thesis relies heavily
on the skip-free property of the random walk. He asked
if one can still reconstruct an i.i.d. scenery seen
along the path of a non-skip-free random walk. In this
article, we positively answer this question. We prove
that if there are enough colors and if the random walk
is recurrent with at most bounded jumps, and if it can
reach every integer, then one can almost surely
reconstruct almost every scenery up to translations and
reflections. Our reconstruction method works if there
are more colors in the scenery than possible single
steps for the random walk.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "ergodic theory; jumps; random walk; Scenery
reconstruction; stationary processes",
}
@Article{Barral:2004:MAC,
author = "Julien Barral and Jacques V{\'e}hel",
title = "Multifractal Analysis of a Class of Additive Processes
with Correlated Non-Stationary Increments",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "16:508--16:543",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-208",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/208",
abstract = "We consider a family of stochastic processes built
from infinite sums of independent positive random
functions on $ R_+ $. Each of these functions increases
linearly between two consecutive negative jumps, with
the jump points following a Poisson point process on $
R_+ $. The motivation for studying these processes
stems from the fact that they constitute simplified
models for TCP traffic on the Internet. Such processes
bear some analogy with L{\'e}vy processes, but they are
more complex in the sense that their increments are
neither stationary nor independent. Nevertheless, we
show that their multifractal behavior is very much the
same as that of certain L{\'e}vy processes. More
precisely, we compute the Hausdorff multifractal
spectrum of our processes, and find that it shares the
shape of the spectrum of a typical L{\'e}vy process.
This result yields a theoretical basis to the empirical
discovery of the multifractal nature of TCP traffic.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Shao:2004:ADB,
author = "Qi-Man Shao and Chun Su and Gang Wei",
title = "Asymptotic Distributions and {Berry--Ess{\'e}en}
Bounds for Sums of Record Values",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "17:544--17:559",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-210",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/210",
abstract = "Let $ \{ U_n, n \geq 1 \} $ be independent uniformly
distributed random variables, and $ \{ Y_n, n \geq 1 \}
$ be independent and identically distributed
non-negative random variables with finite third
moments. Denote $ S_n = \sum_{i = 1}^n Y_i $ and assume
that $ (U_1, \cdots, U_n) $ and $ S_{n + 1} $ are
independent for every fixed $n$. In this paper we
obtain {Berry--Ess{\'e}en} bounds for $ \sum_{i = 1}^n
\psi (U_i S_{n + 1})$, where $ \psi $ is a non-negative
function. As an application, we give
{Berry--Ess{\'e}en} bounds and asymptotic distributions
for sums of record values.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Kouritzin:2004:NFR,
author = "Michael Kouritzin and Wei Sun and Jie Xiong",
title = "Nonliner Filtering for Reflecting Diffusions in Random
Environments via Nonparametric Estimation",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "18:560--18:574",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-214",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
note = "See erratum \cite{Kouritzin:2017:ENF}.",
URL = "http://ejp.ejpecp.org/article/view/214",
abstract = "We study a nonlinear filtering problem in which the
signal to be estimated is a reflecting diffusion in a
random environment. Under the assumption that the
observation noise is independent of the signal, we
develop a nonparametric functional estimation method
for finding workable approximate solutions to the
conditional distributions of the signal state.
Furthermore, we show that the pathwise average
distance, per unit time, of the approximate filter from
the optimal filter is asymptotically small in time.
Also, we use simulations based upon a particle filter
algorithm to show the efficiency of the method.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Bertoin:2004:ALN,
author = "Jean Bertoin and Alexander Gnedin",
title = "Asymptotic Laws for Nonconservative Self-similar
Fragmentations",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "19:575--19:593",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-215",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/215",
abstract = "We consider a self-similar fragmentation process in
which the generic particle of mass $x$ is replaced by
the offspring particles at probability rate $ x^\alpha
$, with positive parameter $ \alpha $. The total of
offspring masses may be both larger or smaller than $x$
with positive probability. We show that under certain
conditions the typical mass in the ensemble is of the
order $ t^{-1 / \alpha }$ and that the empirical
distribution of masses converges to a random limit
which we characterise in terms of the reproduction
law.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Nualart:2004:LSM,
author = "Eulalia Nualart and Thomas Mountford",
title = "Level Sets of Multiparameter {Brownian} Motions",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "20:594--20:614",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-169",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/169",
abstract = "We use Girsanov's theorem to establish a conjecture of
Khoshnevisan, Xiao and Zhong that $ \phi (r) = r^{N - d
/ 2} (\log \log (\frac {1}{r}))^{d / 2} $ is the exact
Hausdorff measure function for the zero level set of an
$N$-parameter $d$-dimensional additive Brownian motion.
We extend this result to a natural multiparameter
version of Taylor and Wendel's theorem on the
relationship between Brownian local time and the
Hausdorff $ \phi $-measure of the zero set.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "additive Brownian motion; Hausdorff measure; level
sets; Local times",
}
@Article{Krylov:2004:QIS,
author = "N. V. Krylov",
title = "Quasiderivatives and Interior Smoothness of Harmonic
Functions Associated with Degenerate Diffusion
Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "21:615--21:633",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-219",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/219",
abstract = "Proofs and two applications of two general results are
given concerning the problem of establishing interior
smoothness of probabilistic solutions of elliptic
degenerate equations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Bass:2004:CSD,
author = "Richard Bass and Edwin Perkins",
title = "Countable Systems of Degenerate Stochastic
Differential Equations with Applications to
Super-{Markov} Chains",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "22:634--22:673",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-222",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/222",
abstract = "We prove well-posedness of the martingale problem for
an infinite-dimensional degenerate elliptic operator
under appropriate H{\"o}lder continuity conditions on
the coefficients. These martingale problems include
large population limits of branching particle systems
on a countable state space in which the particle
dynamics and branching rates may depend on the entire
population in a H{\"o}lder fashion. This extends an
approach originally used by the authors in finite
dimensions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Denis:2004:GAR,
author = "Laurent Denis and L. Stoica",
title = "A General Analytical Result for Non-linear {SPDE}'s
and Applications",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "23:674--23:709",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-223",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/223",
abstract = "Using analytical methods, we prove existence
uniqueness and estimates for s.p.d.e. of the type\par
$$ d u_t + A u_t d t + f (t, u_t) d t + R g(t, u_t) d
t = h(t, x, u_t) d B_t, $$
where $A$ is a linear non-negative self-adjoint
(unbounded) operator, $f$ is a nonlinear function which
depends on $u$ and its derivatives controlled by $
\sqrt {A} u$, $ R g$ corresponds to a nonlinearity
involving $u$ and its derivatives of the same order as
$ A u$ but of smaller magnitude, and the right term
contains a noise involving a $d$-dimensional Brownian
motion multiplied by a non-linear function. We give a
neat condition concerning the magnitude of these
nonlinear perturbations. We also mention a few examples
and, in the case of a diffusion generator, we give a
double stochastic interpretation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{vanderHofstad:2004:GSC,
author = "Remco van der Hofstad and Akira Sakai",
title = "{Gaussian} Scaling for the Critical Spread-out Contact
Process above the Upper Critical Dimension",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "24:710--24:769",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-224",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/224",
abstract = "We consider the critical spread-out contact process in
$ Z^d $ with $ d \geq 1 $, whose infection range is
denoted by $ L \geq 1 $. The two-point function $
\tau_t(x) $ is the probability that $ x \in Z^d $ is
infected at time $t$ by the infected individual located
at the origin $ o \in Z^d$ at time 0. We prove Gaussian
behaviour for the two-point function with $ L \geq L_0$
for some finite $ L_0 = L_0 (d)$ for $ d > 4$. When $ d
\leq 4$, we also perform a local mean-field limit to
obtain Gaussian behaviour for $ \tau_{ tT}(x)$ with $ t
> 0$ fixed and $ T \to \infty $ when the infection
range depends on $T$ in such a way that $ L_T = L T^b$
for any $ b > (4 - d) / 2 d$.\par
The proof is based on the lace expansion and an
adaptation of the inductive approach applied to the
discretized contact process. We prove the existence of
several critical exponents and show that they take on
their respective mean-field values. The results in this
paper provide crucial ingredients to prove convergence
of the finite-dimensional distributions for the contact
process towards those for the canonical measure of
super-Brownian motion, which we defer to a sequel of
this paper.\par
The results in this paper also apply to oriented
percolation, for which we reprove some of the results
in \cite{hs01} and extend the results to the local
mean-field setting described above when $ d \leq 4$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Berestycki:2004:EFC,
author = "Julien Berestycki",
title = "Exchangeable Fragmentation--Coalescence Processes and
their Equilibrium Measures",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "25:770--25:824",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-227",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/227",
abstract = "We define and study a family of Markov processes with
state space the compact set of all partitions of $N$
that we call exchangeable fragmentation-coalescence
processes. They can be viewed as a combination of
homogeneous fragmentation as defined by Bertoin and of
homogeneous coalescence as defined by Pitman and
Schweinsberg or M{\"o}hle and Sagitov. We show that
they admit a unique invariant probability measure and
we study some properties of their paths and of their
equilibrium measure.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Peres:2004:MTR,
author = "Yuval Peres and David Revelle",
title = "Mixing Times for Random Walks on Finite Lamplighter
Groups",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "26:825--26:845",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-198",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/198",
abstract = "Given a finite graph $G$, a vertex of the lamplighter
graph $ G^\diamondsuit = \mathbb {Z}_2 \wr G$ consists
of a zero-one labeling of the vertices of $G$, and a
marked vertex of $G$. For transitive $G$ we show that,
up to constants, the relaxation time for simple random
walk in $ G^\diamondsuit $ is the maximal hitting time
for simple random walk in $G$, while the mixing time in
total variation on $ G^\diamondsuit $ is the expected
cover time on $G$. The mixing time in the uniform
metric on $ G^\diamondsuit $ admits a sharp threshold,
and equals $ |G|$ multiplied by the relaxation time on
$G$, up to a factor of $ \log |G|$. For $ \mathbb {Z}_2
\wr \mathbb {Z}_n^2$, the lamplighter group over the
discrete two dimensional torus, the relaxation time is
of order $ n^2 \log n$, the total variation mixing time
is of order $ n^2 \log^2 n$, and the uniform mixing
time is of order $ n^4$. For $ \mathbb {Z}_2 \wr
\mathbb {Z}_n^d$ when $ d \geq 3$, the relaxation time
is of order $ n^d$, the total variation mixing time is
of order $ n^d \log n$, and the uniform mixing time is
of order $ n^{d + 2}$. In particular, these three
quantities are of different orders of magnitude.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "cover time; lamplighter group; mixing time; random
walks",
}
@Article{Lawler:2004:BEC,
author = "Gregory Lawler and Vlada Limic",
title = "The {Beurling} Estimate for a Class of Random Walks",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "27:846--27:861",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-228",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/228",
abstract = "An estimate of Beurling states that if $K$ is a curve
from $0$ to the unit circle in the complex plane, then
the probability that a Brownian motion starting at $ -
\varepsilon $ reaches the unit circle without hitting
the curve is bounded above by $ c \varepsilon^{1 / 2}$.
This estimate is very useful in analysis of boundary
behavior of conformal maps, especially for connected
but rough boundaries. The corresponding estimate for
simple random walk was first proved by Kesten. In this
note we extend this estimate to random walks with zero
mean, finite $ (3 + \delta)$-moment.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Beurling projection; escape probabilities; Green's
function; random walk",
}
@Article{Puhalskii:2004:SDL,
author = "Anatolii Puhalskii",
title = "On Some Degenerate Large Deviation Problems",
journal = j-ELECTRON-J-PROBAB,
volume = "9",
pages = "28:862--28:886",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v9-232",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/232",
abstract = "This paper concerns the issue of obtaining the large
deviation principle for solutions of stochastic
equations with possibly degenerate coefficients.
Specifically, we explore the potential of the
methodology that consists in establishing exponential
tightness and identifying the action functional via a
maxingale problem. In the author's earlier work it has
been demonstrated that certain convergence properties
of the predictable characteristics of semimartingales
ensure both that exponential tightness holds and that
every large deviation accumulation point is a solution
to a maxingale problem. The focus here is on the
uniqueness for the maxingale problem. It is first shown
that under certain continuity hypotheses existence and
uniqueness of a solution to a maxingale problem of
diffusion type are equivalent to Luzin weak existence
and uniqueness, respectively, for the associated
idempotent It{\^o} equation. Consequently, if the
idempotent equation has a unique Luzin weak solution,
then the action functional is specified uniquely, so
the large deviation principle follows. Two kinds of
application are considered. Firstly, we obtain results
on the logarithmic asymptotics of moderate deviations
for stochastic equations with possibly degenerate
diffusion coefficients which, as compared with earlier
results, relax the growth conditions on the
coefficients, permit certain non-Lipshitz-continuous
coefficients, and allow the coefficients to depend on
the entire past of the process and to be discontinuous
functions of time. The other application concerns
multiple-server queues with impatient customers.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Kim:2005:ESD,
author = "Kyeong-Hun Kim",
title = "{$ L_p $}-Estimates for {SPDE} with Discontinuous
Coefficients in Domains",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "1:1--1:20",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-234",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/234",
abstract = "Stochastic partial differential equations of
divergence form with discontinuous and unbounded
coefficients are considered in $ C^1 $ domains.
Existence and uniqueness results are given in weighted
$ L_p $ spaces, and Holder type estimates are
presented.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "stochastic partial differential equations,
discontinuous coefficients",
}
@Article{Newman:2005:CCN,
author = "Charles Newman and Krishnamurthi Ravishankar and
Rongfeng Sun",
title = "Convergence of Coalescing Nonsimple Random Walks to
the {Brownian Web}",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "2:21--2:60",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-235",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/235",
abstract = "The Brownian Web (BW) is a family of coalescing
Brownian motions starting from every point in space and
time $ R \times R $. It was first introduced by
Arratia, and later analyzed in detail by Toth and
Werner. More recently, Fontes, Isopi, Newman and
Ravishankar (FINR) gave a characterization of the BW,
and general convergence criteria allowing in principle
either crossing or noncrossing paths, which they
verified for coalescing simple random walks. Later
Ferrari, Fontes, and Wu verified these criteria for a
two dimensional Poisson Tree. In both cases, the paths
are noncrossing. To date, the general convergence
criteria of FINR have not been verified for any case
with crossing paths, which appears to be significantly
more difficult than the noncrossing paths case.
Accordingly, in this paper, we formulate new
convergence criteria for the crossing paths case, and
verify them for non-simple coalescing random walks
satisfying a finite fifth moment condition. This is the
first time that convergence to the BW has been proved
for models with crossing paths. Several corollaries are
presented, including an analysis of the scaling limit
of voter model interfaces that extends a result of Cox
and Durrett.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian Web, Invariance Principle, Coalescing Random
Walks, Brownian Networks, Continuum Limit",
}
@Article{Kontoyiannis:2005:LDA,
author = "Ioannis Kontoyiannis and Sean Meyn",
title = "Large Deviations Asymptotics and the Spectral Theory
of Multiplicatively Regular {Markov} Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "3:61--3:123",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-231",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/231",
abstract = "In this paper we continue the investigation of the
spectral theory and exponential asymptotics of
primarily discrete-time Markov processes, following
Kontoyiannis and Meyn (2003). We introduce a new family
of nonlinear Lyapunov drift criteria, which
characterize distinct subclasses of geometrically
ergodic Markov processes in terms of simple
inequalities for the nonlinear generator. We
concentrate primarily on the class of multiplicatively
regular Markov processes, which are characterized via
simple conditions similar to (but weaker than) those of
Donsker--Varadhan. For any such process $ \{ \Phi (t)
\} $ with transition kernel $P$ on a general state
space $X$, the following are obtained. Spectral Theory:
For a large class of (possibly unbounded) functionals
$F$ on $X$, the kernel $ \hat P(x, d y) = e^{F(x)} P(x,
d y)$ has a discrete spectrum in an appropriately
defined Banach space. It follows that there exists a
``maximal, '' well-behaved solution to the
``multiplicative Poisson equation, '' defined as an
eigenvalue problem for $ \hat P$. Multiplicative Mean
Ergodic Theorem: Consider the partial sums of this
process with respect to any one of the functionals $F$
considered above. The normalized mean of their moment
generating function (and not the logarithm of the mean)
converges to the above maximal eigenfunction
exponentially fast. Multiplicative regularity: The
Lyapunov drift criterion under which our results are
derived is equivalent to the existence of regeneration
times with finite exponential moments for the above
partial sums. Large Deviations: The sequence of
empirical measures of the process satisfies a large
deviations principle in a topology finer that the usual
tau-topology, generated by the above class of
functionals. The rate function of this LDP is the
convex dual of logarithm of the above maximal
eigenvalue, and it is shown to coincide with the
Donsker--Varadhan rate function in terms of relative
entropy. Exact Large Deviations Asymptotics: The above
partial sums are shown to satisfy an exact large
deviations expansion, analogous to that obtained by
Bahadur and Ranga Rao for independent random
variables.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Markov process, large deviations, entropy, Lyapunov
function, empirical measures, nonlinear generator,
large deviations principle",
}
@Article{Bass:2005:ASI,
author = "Richard Bass and Jay Rosen",
title = "An Almost Sure Invariance Principle for Renormalized
Intersection Local Times",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "4:124--4:164",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-236",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/236",
abstract = "Let $ \beta_k(n) $ be the number of self-intersections
of order $k$, appropriately renormalized, for a mean
zero planar random walk with $ 2 + \delta $ moments. On
a suitable probability space we can construct the
random walk and a planar Brownian motion $ W_t$ such
that for each $ k \geq 2$, $ | \beta_k(n) -
\gamma_k(n)| = o(1)$, a.s., where $ \gamma_k(n)$ is the
renormalized self-intersection local time of order $k$
at time 1 for the Brownian motion $ W_{nt} / \sqrt
n$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Schuhmacher:2005:DEP,
author = "Dominic Schuhmacher",
title = "Distance Estimates for {Poisson} Process
Approximations of Dependent Thinnings",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "5:165--5:201",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-237",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/237",
abstract = "It is well known, that under certain conditions,
gradual thinning of a point process on $ R^d_+ $,
accompanied by a contraction of space to compensate for
the thinning, leads in the weak limit to a Cox process.
In this article, we apply discretization and a result
based on Stein's method to give estimates of the
Barbour--Brown distance $ d_2 $ between the
distribution of a thinned point process and an
approximating Poisson process, and evaluate the
estimates in concrete examples. We work in terms of
two, somewhat different, thinning models. The main
model is based on the usual thinning notion of deleting
points independently according to probabilities
supplied by a random field. In Section 4, however, we
use an alternative thinning model, which can be more
straightforward to apply if the thinning is determined
by point interactions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Eisenbaum:2005:CBG,
author = "Nathalie Eisenbaum",
title = "A Connection between {Gaussian} Processes and {Markov}
Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "6:202--6:215",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-238",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/238",
abstract = "The Green function of a transient symmetric Markov
process can be interpreted as the covariance of a
centered Gaussian process. This relation leads to
several fruitful identities in law. Symmetric Markov
processes and their associated Gaussian process both
benefit from these connections. Therefore it is of
interest to characterize the associated Gaussian
processes. We present here an answer to that
question.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Cancrini:2005:DLT,
author = "Nicoletta Cancrini and Filippo Cesi and Cyril
Roberto",
title = "Diffusive Long-time Behavior of {Kawasaki} Dynamics",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "7:216--7:249",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-239",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/239",
abstract = "If $ P_t $ is the semigroup associated with the
Kawasaki dynamics on $ Z^d $ and $f$ is a local
function on the configuration space, then the variance
with respect to the invariant measure $ \mu $ of $ P_t
f$ goes to zero as $ t \to \infty $ faster than $ t^{-d
/ 2 + \varepsilon }$, with $ \varepsilon $ arbitrarily
small. The fundamental assumption is a mixing condition
on the interaction of Dobrushin and Schlosman type.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Heicklen:2005:RPS,
author = "Deborah Heicklen and Christopher Hoffman",
title = "Return Probabilities of a Simple Random Walk on
Percolation Clusters",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "8:250--8:302",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-240",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/240",
abstract = "We bound the probability that a continuous time simple
random walk on the infinite percolation cluster on $
Z^d $ returns to the origin at time $t$. We use this
result to show that in dimensions 5 and higher the
uniform spanning forest on infinite percolation
clusters supported on graphs with infinitely many
connected components a.s.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Birkner:2005:ASB,
author = "Matthias Birkner and Jochen Blath and Marcella Capaldo
and Alison Etheridge and Martin M{\"o}hle and Jason
Schweinsberg and Anton Wakolbinger",
title = "Alpha-Stable Branching and Beta-Coalescents",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "9:303--9:325",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-241",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/241",
abstract = "We determine that the continuous-state branching
processes for which the genealogy, suitably
time-changed, can be described by an autonomous Markov
process are precisely those arising from $ \alpha
$-stable branching mechanisms. The random ancestral
partition is then a time-changed $ \Lambda
$-coalescent, where $ \Lambda $ is the
Beta-distribution with parameters $ 2 - \alpha $ and $
\alpha $, and the time change is given by $ Z^{1 -
\alpha }$, where $Z$ is the total population size. For
$ \alpha = 2$ (Feller's branching diffusion) and $
\Lambda = \delta_0$ (Kingman's coalescent), this is in
the spirit of (a non-spatial version of) Perkins'
Disintegration Theorem. For $ \alpha = 1$ and $ \Lambda
$ the uniform distribution on $ [0, 1]$, this is the
duality discovered by Bertoin \& Le Gall (2000) between
the norming of Neveu's continuous state branching
process and the Bolthausen--Sznitman coalescent.\par
We present two approaches: one, exploiting the
`modified lookdown construction', draws heavily on
Donnelly \& Kurtz (1999); the other is based on direct
calculations with generators.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Berzin:2005:CFM,
author = "Corinne Berzin and Jos{\'e} Le{\'o}n",
title = "Convergence in Fractional Models and Applications",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "10:326--10:370",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-172",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/172",
abstract = "We consider a fractional Brownian motion with Hurst
parameter strictly between 0 and 1. We are interested
in the asymptotic behaviour of functionals of the
increments of this and related processes and we propose
several probabilistic and statistical applications.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "fractional Brownian motion; Level crossings; limit
theorem; local time; rate of convergence",
}
@Article{Salminen:2005:PIF,
author = "Paavo Salminen and Marc Yor",
title = "Perpetual Integral Functionals as Hitting and
Occupation Times",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "11:371--11:419",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-256",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/256",
abstract = "Let $X$ be a linear diffusion and $f$ a non-negative,
Borel measurable function. We are interested in finding
conditions on $X$ and $f$ which imply that the
perpetual integral functional\par
$$ I^X_\infty (f) := \int_0^\infty f(X_t) d t $$
is identical in law with the first hitting time of a
point for some other diffusion. This phenomenon may
often be explained using random time change. Because of
some potential applications in mathematical finance, we
are considering mainly the case when $X$ is a Brownian
motion with drift $ \mu > 0, $ denoted $ {B^{(\mu)}_t
\colon t \geq 0}, $ but it is obvious that the method
presented is more general. We also review the known
examples and give new ones. In particular, results
concerning one-sided functionals\par
$$ \int_0^\infty f(B^{(\mu)}_t){\bf 1}_{{B^{(\mu)}_t <
0}} d t \quad {\rm and} \quad \int_0^\infty
f(B^{(\mu)}_t){\bf 1}_{{B^{(\mu)}_t > 0}} d t $$
are presented. This approach generalizes the proof,
based on the random time change techniques, of the fact
that the Dufresne functional (this corresponds to $
f(x) = \exp ( - 2 x)), $ playing quite an important
role in the study of geometric Brownian motion, is
identical in law with the first hitting time for a
Bessel process. Another functional arising naturally in
this context is\par
$$ \int_0^\infty \big (a + \exp (B^{(\mu)}_t)
\big)^{-2} d t, $$
which is seen, in the case $ \mu = 1 / 2, $ to be
identical in law with the first hitting time for a
Brownian motion with drift $ \mu = a / 2.$ The paper is
concluded by discussing how the Feynman--Kac formula
can be used to find the distribution of a perpetual
integral functional.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Chauvin:2005:MPB,
author = "B. Chauvin and T. Klein and J.-F. Marckert and A.
Rouault",
title = "Martingales and Profile of Binary Search Trees",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "12:420--12:435",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-257",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/257",
abstract = "We are interested in the asymptotic analysis of the
binary search tree (BST) under the random permutation
model. Via an embedding in a continuous time model, we
get new results, in particular the asymptotic behavior
of the profile.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Mountford:2005:TCN,
author = "Thomas Mountford and Li-Chau Wu",
title = "The Time for a Critical Nearest Particle System to
reach Equilibrium starting with a large Gap",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "13:436--13:498",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-242",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/242",
abstract = "We consider the time for a critical nearest particle
system, starting in equilibrium subject to possessing a
large gap, to achieve equilibrium.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Interacting Particle Systems, Reversibility,
Convergence to equilibrium",
}
@Article{Panchenko:2005:CLT,
author = "Dmitry Panchenko",
title = "A {Central Limit Theorem} for Weighted Averages of
Spins in the High Temperature Region of the
{Sherrington--Kirkpatrick} Model",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "14:499--14:524",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-258",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/258",
abstract = "In this paper we prove that in the high temperature
region of the Sherrington--Kirkpatrick model for a
typical realization of the disorder the weighted
average of spins $ \sum_{i \leq N} t_i \sigma_i $ will
be approximately Gaussian provided that $ \max_{i \leq
N}|t_i| / \sum_{i \leq N} t_i^2 $ is small.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{DaiPra:2005:LSI,
author = "Paolo {Dai Pra} and Gustavo Posta",
title = "Logarithmic {Sobolev} Inequality for Zero--Range
Dynamics: Independence of the Number of Particles",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "15:525--15:576",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-259",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/259",
abstract = "We prove that the logarithmic-Sobolev constant for
Zero-Range Processes in a box of diameter $L$ may
depend on $L$ but not on the number of particles. This
is a first, but relevant and quite technical step, in
the proof that this logarithmic-Sobolev constant grows
as the square of $L$, that is presented in a
forthcoming paper.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Chen:2005:LDL,
author = "Xia Chen and Wenbo Li and Jay Rosen",
title = "Large Deviations for Local Times of Stable Processes
and Stable Random Walks in 1 Dimension",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "16:577--16:608",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-260",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/260",
abstract = "In Chen and Li (2004), large deviations were obtained
for the spatial $ L^p $ norms of products of
independent Brownian local times and local times of
random walks with finite second moment. The methods of
that paper depended heavily on the continuity of the
Brownian path and the fact that the generator of
Brownian motion, the Laplacian, is a local operator. In
this paper we generalize these results to local times
of symmetric stable processes and stable random
walks.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Biggins:2005:FPS,
author = "John Biggins and Andreas Kyprianou",
title = "Fixed Points of the Smoothing Transform: the Boundary
Case",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "17:609--17:631",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-255",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/255",
abstract = "Let $ A = (A_1, A_2, A_3, \ldots) $ be a random
sequence of non-negative numbers that are ultimately
zero with $ E[\sum A_i] = 1 $ and $ E \left [\sum A_i
\log A_i \right] \leq 0 $. The uniqueness of the
non-negative fixed points of the associated smoothing
transform is considered. These fixed points are
solutions to the functional equation $ \Phi (\psi) = E
\left [\prod_i \Phi (\psi A_i) \right], $ where $ \Phi
$ is the Laplace transform of a non-negative random
variable. The study complements, and extends, existing
results on the case when $ E \left [\sum A_i \log A_i
\right] < 0 $. New results on the asymptotic behaviour
of the solutions near zero in the boundary case, where
$ E \left [\sum A_i \log A_i \right] = 0 $, are
obtained.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "branching random walk; functional equation; Smoothing
transform",
}
@Article{Cabanal-Duvillard:2005:MRB,
author = "Thierry Cabanal-Duvillard",
title = "A Matrix Representation of the {Bercovici--Pata}
Bijection",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "18:632--18:661",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-246",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/246",
abstract = "Let $ \mu $ be an infinitely divisible law on the real
line, $ \Lambda (\mu) $ its freely infinitely divisible
image by the Bercovici--Pata bijection. The purpose of
this article is to produce a new kind of random
matrices with distribution $ \mu $ at dimension 1, and
with its empirical spectral law converging to $ \Lambda
(\mu) $ as the dimension tends to infinity. This
constitutes a generalisation of Wigner's result for the
Gaussian Unitary Ensemble.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Random matrices, free probability, infinitely
divisible laws",
}
@Article{Lozada-Chang:2005:LDM,
author = "Li-Vang Lozada-Chang",
title = "Large Deviations on Moment Spaces",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "19:662--19:690",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-202",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/202",
abstract = "In this paper we study asymptotic behavior of some
moment spaces. We consider two different settings. In
the first one, we work with ordinary multi-dimensional
moments on the standard $m$-simplex. In the second one,
we deal with the trigonometric moments on the unit
circle of the complex plane. We state large and
moderate deviation principles for uniformly distributed
moments. In both cases the rate function of the large
deviation principle is related to the reversed Kullback
information with respect to the uniform measure on the
integration space.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "large deviations; multidimensional moment; random
moment problem",
}
@Article{Begyn:2005:QVA,
author = "Arnaud Begyn",
title = "Quadratic Variations along Irregular Subdivisions for
{Gaussian} Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "20:691--20:717",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-245",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/245",
abstract = "In this paper we deal with second order quadratic
variations along general subdivisions for processes
with Gaussian increments. These have almost surely a
deterministic limit under conditions on the mesh of the
subdivisions. This limit depends on the singularity
function of the process and on the structure of the
subdivisions too. Then we illustrate the results with
the example of the time-space deformed fractional
Brownian motion and we present some simulations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "estimation, fractional processes, Gaussian processes,
generalized quadratic variations, irregular
subdivisions, singularity function",
}
@Article{Goldschmidt:2005:RRT,
author = "Christina Goldschmidt and James Martin",
title = "Random Recursive Trees and the {Bolthausen--Sznitman}
Coalesent",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "21:718--21:745",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-265",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/265",
abstract = "We describe a representation of the
Bolthausen--Sznitman coalescent in terms of the cutting
of random recursive trees. Using this representation,
we prove results concerning the final collision of the
coalescent restricted to $ [n] $: we show that the
distribution of the number of blocks involved in the
final collision converges as $ n \to \infty $, and
obtain a scaling law for the sizes of these blocks. We
also consider the discrete-time Markov chain giving the
number of blocks after each collision of the coalescent
restricted to $ [n] $; we show that the transition
probabilities of the time-reversal of this Markov chain
have limits as $ n \to \infty $. These results can be
interpreted as describing a ``post-gelation'' phase of
the Bolthausen--Sznitman coalescent, in which a giant
cluster containing almost all of the mass has already
formed and the remaining small blocks are being
absorbed.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Bouchard:2005:HAO,
author = "Bruno Bouchard and Emmanuel Teman",
title = "On the Hedging of {American} Options in Discrete Time
with Proportional Transaction Costs",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "22:746--22:760",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-266",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/266",
abstract = "In this note, we consider a general discrete time
financial market with proportional transaction costs as
in Kabanov and Stricker (2001), Kabanov et al. (2002),
Kabanov et al. (2003) and Schachermayer (2004). We
provide a dual formulation for the set of initial
endowments which allow to super-hedge some American
claim. We show that this extends the result of
Chalasani and Jha (2001) which was obtained in a model
with constant transaction costs and risky assets which
evolve on a finite dimensional tree. We also provide
fairly general conditions under which the expected
formulation in terms of stopping times does not work.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Coutin:2005:SMR,
author = "Laure Coutin and Antoine Lejay",
title = "Semi-martingales and rough paths theory",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "23:761--23:785",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-162",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/162",
abstract = "We prove that the theory of rough paths, which is used
to define path-wise integrals and path-wise
differential equations, can be used with continuous
semi-martingales. We provide then an almost sure
theorem of type Wong--Zakai. Moreover, we show that the
conditions UT and UCV, used to prove that one can
interchange limits and It{\^o} or Stratonovich
integrals, provide the same result when one uses the
rough paths theory.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "$p$-variation; conditions UT and UCV; iterated
integrals; rough paths; Semi-martingales; Wong--Zakai
theorem",
}
@Article{Cassandro:2005:ODR,
author = "Marzio Cassandro and Enza Orlandi and Pierre Picco and
Maria Eulalia Vares",
title = "One-dimensional Random Field {Kac}'s Model:
Localization of the Phases",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "24:786--24:864",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-263",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/263",
abstract = "We study the typical profiles of a one dimensional
random field Kac model, for values of the temperature
and magnitude of the field in the region of two
absolute minima for the free energy of the
corresponding random field Curie Weiss model. We show
that, for a set of realizations of the random field of
overwhelming probability, the localization of the two
phases corresponding to the previous minima is
completely determined. Namely, we are able to construct
random intervals tagged with a sign, where typically,
with respect to the infinite volume Gibbs measure, the
profile is rigid and takes, according to the sign, one
of the two values corresponding to the previous minima.
Moreover, we characterize the transition from one phase
to the other. The analysis extends the one done by
Cassandro, Orlandi and Picco in [13].",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Phase transition, random walk, random environment, Kac
potential",
}
@Article{Flandoli:2005:SVF,
author = "Franco Flandoli and Massimiliano Gubinelli",
title = "Statistics of a Vortex Filament Model",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "25:865--25:900",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-267",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/267",
abstract = "A random incompressible velocity field in three
dimensions composed by Poisson distributed Brownian
vortex filaments is constructed. The filaments have a
random thickness, length and intensity, governed by a
measure $ \gamma $. Under appropriate assumptions on $
\gamma $ we compute the scaling law of the structure
function of the field and show that, in particular, it
allows for either K41-like scaling or multifractal
scaling.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Fulman:2005:SMD,
author = "Jason Fulman",
title = "{Stein}'s Method and Descents after Riffle Shuffles",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "26:901--26:924",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-268",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/268",
abstract = "Berestycki and Durrett used techniques from random
graph theory to prove that the distance to the identity
after iterating the random transposition shuffle
undergoes a transition from Poisson to normal behavior.
This paper establishes an analogous result for distance
after iterates of riffle shuffles or iterates of riffle
shuffles and cuts. The analysis uses different tools:
Stein's method and generating functions. A useful
technique which emerges is that of making a problem
more tractable by adding extra symmetry, then using
Stein's method to exploit the symmetry in the modified
problem, and from this deducing information about the
original problem.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Csaki:2005:IPV,
author = "Endre Csaki and Yueyun Hu",
title = "On the Increments of the Principal Value of {Brownian}
Local Time",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "27:925--27:947",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-269",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/269",
abstract = "Let $W$ be a one-dimensional Brownian motion starting
from 0. Define $ Y(t) = \int_0^t{ds \over W(s)} :=
\lim_{\epsilon \to 0} \int_0^t 1_{(|W(s)| > \epsilon)}
{ds \over W(s)}$ as Cauchy's principal value related to
local time. We prove limsup and liminf results for the
increments of $Y$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Chaumont:2005:LPC,
author = "Lo{\"\i}c Chaumont and Ronald Doney",
title = "On {L{\'e}vy} processes conditioned to stay positive",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "28:948--28:961",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-261",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
note = "See corrections \cite{Chaumont:2008:CLP}.",
URL = "http://ejp.ejpecp.org/article/view/261",
abstract = "We construct the law of L{\'e}vy processes conditioned
to stay positive under general hypotheses. We obtain a
Williams type path decomposition at the minimum of
these processes. This result is then applied to prove
the weak convergence of the law of L{\'e}vy processes
conditioned to stay positive as their initial state
tends to 0. We describe an absolute continuity
relationship between the limit law and the measure of
the excursions away from 0 of the underlying L{\'e}vy
process reflected at its minimum. Then, when the
L{\'e}vy process creeps upwards, we study the lower
tail at 0 of the law of the height of this excursion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "L'evy process conditioned to stay positive, path
decomposition, weak convergence, excursion measure,
creeping",
}
@Article{Posta:2005:EFO,
author = "Gustavo Posta",
title = "Equilibrium Fluctuations for a One-Dimensional
Interface in the Solid on Solid Approximation",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "29:962--29:987",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-270",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/270",
abstract = "An unbounded one-dimensional solid-on-solid model with
integer heights is studied. Unbounded here means that
there is no {\em a priori} restrictions on the discrete
gradient of the interface. The interaction Hamiltonian
of the interface is given by a finite range part,
proportional to the sum of height differences, plus a
part of exponentially decaying long range potentials.
The evolution of the interface is a reversible Markov
process. We prove that if this system is started in the
center of a box of size $L$ after a time of order $
L^3$ it reaches, with a very large probability, the top
or the bottom of the box.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Bahlali:2005:GSM,
author = "Seid Bahlali and Brahim Mezerdi",
title = "A General Stochastic Maximum Principle for Singular
Control Problems",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "30:988--30:1004",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-271",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/271",
abstract = "We consider the stochastic control problem in which
the control domain need not be convex, the control
variable has two components, the first being absolutely
continuous and the second singular. The coefficients of
the state equation are non linear and depend explicitly
on the absolutely continuous component of the control.
We establish a maximum principle, by using a spike
variation on the absolutely continuous part of the
control and a convex perturbation on the singular one.
This result is a generalization of Peng's maximum
principle to singular control problems.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Chorro:2005:CDL,
author = "Christophe Chorro",
title = "Convergence in {Dirichlet} Law of Certain Stochastic
Integrals",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "31:1005--31:1025",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-272",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/272",
abstract = "Recently, Nicolas Bouleau has proposed an extension of
the Donsker's invariance principle in the framework of
Dirichlet forms. He proves that an erroneous random
walk of i.i.d random variables converges in Dirichlet
law toward the Ornstein--Uhlenbeck error structure on
the Wiener space. The aim of this paper is to extend
this result to some families of stochastic integrals.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Ganesh:2005:SPL,
author = "Ayalvadi Ganesh and Claudio Macci and Giovanni
Torrisi",
title = "Sample Path Large Deviations Principles for {Poisson}
Shot Noise Processes and Applications",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "32:1026--32:1043",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-273",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/273",
abstract = "This paper concerns sample path large deviations for
Poisson shot noise processes, and applications in
queueing theory. We first show that, under an
exponential tail condition, Poisson shot noise
processes satisfy a sample path large deviations
principle with respect to the topology of pointwise
convergence. Under a stronger superexponential tail
condition, we extend this result to the topology of
uniform convergence. We also give applications of this
result to determining the most likely path to overflow
in a single server queue, and to finding tail
asymptotics for the queue lengths at priority queues.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "large deviations; Poisson shot noise; queues; risk;
sample paths",
}
@Article{Bell:2005:DSP,
author = "Steven Bell and Ruth Williams",
title = "Dynamic Scheduling of a Parallel Server System in
Heavy Traffic with Complete Resource Pooling:
Asymptotic Optimality of a Threshold Policy",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "33:1044--33:1115",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-281",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/281",
abstract = "We consider a parallel server queueing system
consisting of a bank of buffers for holding incoming
jobs and a bank of flexible servers for processing
these jobs. Incoming jobs are classified into one of
several different classes (or buffers). Jobs within a
class are processed on a first-in-first-out basis,
where the processing of a given job may be performed by
any server from a given (class-dependent) subset of the
bank of servers. The random service time of a job may
depend on both its class and the server providing the
service. Each job departs the system after receiving
service from one server. The system manager seeks to
minimize holding costs by dynamically scheduling
waiting jobs to available servers. We consider a
parameter regime in which the system satisfies both a
heavy traffic and a complete resource pooling
condition. Our cost function is an expected cumulative
discounted cost of holding jobs in the system, where
the (undiscounted) cost per unit time is a linear
function of normalized (with heavy traffic scaling)
queue length. In a prior work, the second author
proposed a continuous review threshold control policy
for use in such a parallel server system. This policy
was advanced as an ``interpretation'' of the analytic
solution to an associated Brownian control problem
(formal heavy traffic diffusion approximation). In this
paper we show that the policy proposed previously is
asymptotically optimal in the heavy traffic limit and
that the limiting cost is the same as the optimal cost
in the Brownian control problem.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Ledoux:2005:DIE,
author = "Michel Ledoux",
title = "Distributions of Invariant Ensembles from the
Classical Orthogonal Polynimials: the Discrete Case",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "34:1116--34:1146",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-282",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/282",
abstract = "We examine the Charlier, Meixner, Krawtchouk and Hahn
discrete orthogonal polynomial ensembles, deeply
investigated by K. Johansson, using integration by
parts for the underlying Markov operators, differential
equations on Laplace transforms and moment equations.
As for the matrix ensembles, equilibrium measures are
described as limits of empirical spectral
distributions. In particular, a new description of the
equilibrium measures as adapted mixtures of the
universal arcsine law with an independent uniform
distribution is emphasized. Factorial moment identities
on mean spectral measures may be used towards small
deviation inequalities on the rightmost charges at the
rate given by the Tracy--Widom asymptotics.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Durrett:2005:CSB,
author = "Richard Durrett and Leonid Mytnik and Edwin Perkins",
title = "Competing super-{Brownian} motions as limits of
interacting particle systems",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "35:1147--35:1220",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-229",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/229",
abstract = "We study two-type branching random walks in which the
birth or death rate of each type can depend on the
number of neighbors of the opposite type. This
competing species model contains variants of Durrett's
predator-prey model and Durrett and Levin's colicin
model as special cases. We verify in some cases
convergence of scaling limits of these models to a pair
of super-Brownian motions interacting through their
collision local times, constructed by Evans and
Perkins.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "super-Brownian motion, interacting branching particle
systems, collision local time, competing species,
measure-valued diffusions",
}
@Article{Sethuraman:2005:MPD,
author = "Sunder Sethuraman and Srinivasa Varadhan",
title = "A Martingale Proof of {Dobrushin}'s Theorem for
Non-Homogeneous {Markov} Chains",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "36:1221--36:1235",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-283",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/283",
abstract = "In 1956, Dobrushin proved an important central limit
theorem for non-homogeneous Markov chains. In this
note, a shorter and different proof elucidating more
the assumptions is given through martingale
approximation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Ariyoshi:2005:STA,
author = "Teppei Ariyoshi and Masanori Hino",
title = "Small-time Asymptotic Estimates in Local {Dirichlet}
Spaces",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "37:1236--37:1259",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-286",
ISSN = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/286",
abstract = "Small-time asymptotic estimates of semigroups on a
logarithmic scale are proved for all symmetric local
Dirichlet forms on $ \sigma $-finite measure spaces,
which is an extension of the work by Hino and
Ram{\'\i}rez [4].",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Wang:2005:LTS,
author = "Qiying Wang",
title = "Limit Theorems for Self-Normalized Large Deviation",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "38:1260--38:1285",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-289",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/289",
abstract = "Let $ X, X_1, X_2, \cdots $ be i.i.d. random variables
with zero mean and finite variance $ \sigma^2 $. It is
well known that a finite exponential moment assumption
is necessary to study limit theorems for large
deviation for the standardized partial sums. In this
paper, limit theorems for large deviation for
self-normalized sums are derived only under finite
moment conditions. In particular, we show that, if $ E
X^4 < \infty $, then \par
$$ \frac {P(S_n / V_n \geq x)}{1 - \Phi (x)} = \exp
\left \{ - \frac {x^3 EX^3}{3 \sqrt { n} \sigma^3}
\right \} \left [1 + O \left (\frac {1 + x}{\sqrt { n}}
\right) \right], $$
for $ x \ge 0 $ and $ x = O(n^{1 / 6}) $, where $ S_n =
\sum_{i = 1}^n X_i $ and $ V_n = (\sum_{i = 1}^n
X_i^2)^{1 / 2} $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Cram{\'e}r large deviation, limit theorem",
}
@Article{Greven:2005:RTI,
author = "Andreas Greven and Vlada Limic and Anita Winter",
title = "Representation Theorems for Interacting {Moran}
Models, Interacting {Fisher--Wrighter} Diffusions and
Applications",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "39:1286--39:1358",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-290",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/290",
abstract = "We consider spatially interacting Moran models and
their diffusion limit which are interacting
Fisher--Wright diffusions. The Moran model is a spatial
population model with individuals of different type
located on sites given by elements of an Abelian group.
The dynamics of the system consists of independent
migration of individuals between the sites and a
resampling mechanism at each site, i.e., pairs of
individuals are replaced by new pairs where each
newcomer takes the type of a randomly chosen individual
from the parent pair. Interacting Fisher--Wright
diffusions collect the relative frequency of a subset
of types evaluated for the separate sites in the limit
of infinitely many individuals per site. One is
interested in the type configuration as well as the
time-space evolution of genealogies, encoded in the
so-called historical process. The first goal of the
paper is the analytical characterization of the
historical processes for both models as solutions of
well-posed martingale problems and the development of a
corresponding duality theory. For that purpose, we link
both the historical Fisher--Wright diffusions and the
historical Moran models by the so-called look-down
process. That is, for any fixed time, a collection of
historical Moran models with increasing particle
intensity and a particle representation for the
limiting historical interacting Fisher--Wright
diffusions are provided on one and the same probability
space. This leads to a strong form of duality between
spatially interacting Moran models, interacting
Fisher--Wright diffusions on the one hand and
coalescing random walks on the other hand, which
extends the classical weak form of moment duality for
interacting Fisher--Wright diffusions. Our second goal
is to show that this representation can be used to
obtain new results on the long-time behavior, in
particular (i) on the structure of the equilibria, and
of the equilibrium historical processes, and (ii) on
the behavior of our models on large but finite site
space in comparison with our models on infinite site
space. Here the so-called finite system scheme is
established for spatially interacting Moran models
which implies via the look-down representation also the
already known results for interacting Fisher--Wright
diffusions. Furthermore suitable versions of the finite
system scheme on the level of historical processes are
newly developed and verified. In the long run the
provided look-down representation is intended to answer
questions about finer path properties of interacting
Fisher--Wright diffusions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "equilibrium measure; exchangeability; historical
martingale problem; historical process; Interacting
Fischer--Wright diffusions; large finite systems;
look-down construction; spatially interacting Moran
model",
}
@Article{Puchala:2005:EAT,
author = "Zbigniew Puchala and Tomasz Rolski",
title = "The Exact Asymptotic of the Time to Collision",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "40:1359--40:1380",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-291",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/291",
abstract = "In this note we consider the time of the collision $
\tau $ for $n$ independent copies of Markov processes $
X^1_t, \ldots {}, X^n_t$, each starting from $ x_i$,
where $ x_1 < \ldots {} < x_n$. We show that for the
continuous time random walk $ P_x(\tau > t) = t^{-n(n -
1) / 4}(C h(x) + o(1)), $ where $C$ is known and $
h(x)$ is the Vandermonde determinant. From the proof
one can see that the result also holds for $ X_t$ being
the Brownian motion or the Poisson process. An
application to skew standard Young tableaux is given.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion; collision time; continuous time
random walk; skew Young tableaux; tandem queue",
}
@Article{Igloi:2005:ROT,
author = "Endre Igl{\'o}i",
title = "A Rate-Optimal Trigonometric Series Expansion of the
Fractional {Brownian} Motion",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "41:1381--41:1397",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-287",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/287",
abstract = "Let $ B^{(H)}(t), t \in \lbrack - 1, 1] $, be the
fractional Brownian motion with Hurst parameter $ H \in
(1 / 2, 1) $. In this paper we present the series
representation $ B^{(H)}(t) = a_0 t \xi_0 + \sum_{j =
1}^{\infty }a_j((1 - \cos (j \pi t)) \xi_j + \sin (j
\pi t) \widetilde {\xi }_j), t \in \lbrack - 1, 1] $,
where $ a_j, j \in \mathbb {N} \cup {0} $, are
constants given explicitly, and $ \xi_j, j \in \mathbb
{N} \cup {0} $, $ \widetilde {\xi }_j, j \in \mathbb
{N} $, are independent standard Gaussian random
variables. We show that the series converges almost
surely in $ C[ - 1, 1] $, and in mean-square (in $ L^2
(\Omega)$), uniformly in $ t \in \lbrack - 1, 1]$.
Moreover we prove that the series expansion has an
optimal rate of convergence.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "fractional Brownian motion; function series expansion;
Gamma-mixed Ornstein--Uhlenbeck process; rate of
convergence",
}
@Article{Mikulevicius:2005:CDP,
author = "Remigijus Mikulevicius and Henrikas Pragarauskas",
title = "On {Cauchy--Dirichlet} Problem in Half-Space for
Linear Integro-Differential Equations in Weighted
{H{\"o}lder} Spaces",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "42:1398--42:1416",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-292",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/292",
abstract = "We study the Cauchy--Dirichlet problem in half-space
for linear parabolic integro-differential equations.
Sufficient conditions are derived under which the
problem has a unique solution in weighted Hoelder
classes. The result can be used in the regularity
analysis of certain functionals arising in the theory
of Markov processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Markov jump processes, parabolic integro-differential
equations",
}
@Article{Jean:2005:RWG,
author = "Mairesse Jean",
title = "Random Walks on Groups and Monoids with a {Markovian}
Harmonic Measure",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "43:1417--43:1441",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-293",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/293",
abstract = "We consider a transient nearest neighbor random walk
on a group $G$ with finite set of generators $S$. The
pair $ (G, S)$ is assumed to admit a natural notion of
normal form words where only the last letter is
modified by multiplication by a generator. The basic
examples are the free products of a finitely generated
free group and a finite family of finite groups, with
natural generators. We prove that the harmonic measure
is Markovian of a particular type. The transition
matrix is entirely determined by the initial
distribution which is itself the unique solution of a
finite set of polynomial equations of degree two. This
enables to efficiently compute the drift, the entropy,
the probability of ever hitting an element, and the
minimal positive harmonic functions of the walk. The
results extend to monoids.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Finitely generated group or monoid; free product;
harmonic measure.; random walk",
}
@Article{Kozdron:2005:ERW,
author = "Michael Kozdron and Gregory Lawler",
title = "Estimates of Random Walk Exit Probabilities and
Application to Loop-Erased Random Walk",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "44:1442--44:1467",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-294",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/294",
abstract = "We prove an estimate for the probability that a simple
random walk in a simply connected subset $A$ of $ Z^2$
starting on the boundary exits $A$ at another specified
boundary point. The estimates are uniform over all
domains of a given inradius. We apply these estimates
to prove a conjecture of S. Fomin in 2001 concerning a
relationship between crossing probabilities of
loop-erased random walk and Brownian motion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Cvitanic:2005:SDM,
author = "Jaksa Cvitanic and Jianfeng Zhang",
title = "The Steepest Descent Method for Forward--Backward
{SDEs}",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "45:1468--45:1495",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-295",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/295",
abstract = "This paper aims to open a door to Monte-Carlo methods
for numerically solving Forward--Backward SDEs, without
computing over all Cartesian grids as usually done in
the literature. We transform the FBSDE to a control
problem and propose the steepest descent method to
solve the latter one. We show that the original
(coupled) FBSDE can be approximated by {it decoupled}
FBSDEs, which further comes down to computing a
sequence of conditional expectations. The rate of
convergence is obtained, and the key to its proof is a
new well-posedness result for FBSDEs. However, the
approximating decoupled FBSDEs are non-Markovian. Some
Markovian type of modification is needed in order to
make the algorithm efficiently implementable.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Hausenblas:2005:EUR,
author = "Erika Hausenblas",
title = "Existence, Uniqueness and Regularity of Parabolic
{SPDEs} Driven by {Poisson} Random Measure",
journal = j-ELECTRON-J-PROBAB,
volume = "10",
pages = "46:1496--46:1546",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v10-297",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/297",
abstract = "In this paper we investigate SPDEs in certain Banach
spaces driven by a Poisson random measure. We show
existence and uniqueness of the solution, investigate
certain integrability properties and verify the
c{\`a}dl{\`a}g property.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Goel:2006:MTB,
author = "Sharad Goel and Ravi Montenegro and Prasad Tetali",
title = "Mixing Time Bounds via the Spectral Profile",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "1:1--1:26",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-300",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/300",
abstract = "On complete, non-compact manifolds and infinite
graphs, Faber--Krahn inequalities have been used to
estimate the rate of decay of the heat kernel. We
develop this technique in the setting of finite Markov
chains, proving upper and lower $ L^{\infty } $ mixing
time bounds via the spectral profile. This approach
lets us recover and refine previous conductance-based
bounds of mixing time (including the Morris--Peres
result), and in general leads to sharper estimates of
convergence rates. We apply this method to several
models including groups with moderate growth, the
fractal-like Viscek graphs, and the product group $ Z_a
\times Z_b $, to obtain tight bounds on the
corresponding mixing times.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Alsmeyer:2006:SFP,
author = "Gerold Alsmeyer and Uwe R{\"o}sler",
title = "A Stochastic Fixed Point Equation Related to Weighted
Branching with Deterministic Weights",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "2:27--2:56",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-296",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/296",
abstract = "For real numbers $ C, T_1, T_2, \ldots {} $ we find
all solutions $ \mu $ to the stochastic fixed point
equation $ W \sim \sum_{j \ge 1}T_j W_j + C $, where $
W, W_1, W_2, \ldots {} $ are independent real-valued
random variables with distribution $ \mu $ and $ \sim $
means equality in distribution. All solutions are
infinitely divisible. The set of solutions depends on
the closed multiplicative subgroup of $ { R}_*= { R}
\backslash \{ 0 \} $ generated by the $ T_j $. If this
group is continuous, i.e., $ {R}_* $ itself or the
positive half line $ {R}_+ $, then all nontrivial fixed
points are stable laws. In the remaining (discrete)
cases further periodic solutions arise. A key
observation is that the Levy measure of any fixed point
is harmonic with respect to $ \Lambda = \sum_{j \ge 1}
\delta_{T_j} $, i.e., $ \Gamma = \Gamma \star \Lambda
$, where $ \star $ means multiplicative convolution.
This will enable us to apply the powerful Choquet--Deny
theorem.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Choquet--Deny theorem; infinite divisibility; L'evy
measure; stable distribution; Stochastic fixed point
equation; weighted branching process",
}
@Article{Cheridito:2006:DMR,
author = "Patrick Cheridito and Freddy Delbaen and Michael
Kupper",
title = "Dynamic Monetary Risk Measures for Bounded
Discrete-Time Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "3:57--3:106",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-302",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/302",
abstract = "We study dynamic monetary risk measures that depend on
bounded discrete-time processes describing the
evolution of financial values. The time horizon can be
finite or infinite. We call a dynamic risk measure
time-consistent if it assigns to a process of financial
values the same risk irrespective of whether it is
calculated directly or in two steps backwards in time.
We show that this condition translates into a
decomposition property for the corresponding acceptance
sets, and we demonstrate how time-consistent dynamic
monetary risk measures can be constructed by pasting
together one-period risk measures. For conditional
coherent and convex monetary risk measures, we provide
dual representations of Legendre--Fenchel type based on
linear functionals induced by adapted increasing
processes of integrable variation. Then we give dual
characterizations of time-consistency for dynamic
coherent and convex monetary risk measures. To this
end, we introduce a concatenation operation for adapted
increasing processes of integrable variation, which
generalizes the pasting of probability measures. In the
coherent case, time-consistency corresponds to
stability under concatenation in the dual. For dynamic
convex monetary risk measures, the dual
characterization of time-consistency generalizes to a
condition on the family of convex conjugates of the
conditional risk measures at different times. The
theoretical results are applied by discussing the
time-consistency of various specific examples of
dynamic monetary risk measures that depend on bounded
discrete-time processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Tang:2006:IND,
author = "Qihe Tang",
title = "Insensitivity to Negative Dependence of the Asymptotic
Behavior of Precise Large Deviations",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "4:107--4:120",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-304",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/304",
abstract = "Since the pioneering works of C. C. Heyde, A. V.
Nagaev, and S. V. Nagaev in 1960's and 1970's, the
precise asymptotic behavior of large-deviation
probabilities of sums of heavy-tailed random variables
has been extensively investigated by many people, but
mostly it is assumed that the random variables under
discussion are independent. In this paper, we extend
the study to the case of negatively dependent random
variables and we find out that the asymptotic behavior
of precise large deviations is insensitive to the
negative dependence.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "(lower/upper) negative dependence; (upper) Matuszewska
index; Consistent variation; partial sum; precise large
deviations; uniform asymptotics",
}
@Article{Hamadene:2006:BTR,
author = "Said Hamadene and Mohammed Hassani",
title = "{BSDEs} with two reflecting barriers driven by a
{Brownian} motion and {Poisson} noise and related
{Dynkin} game",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "5:121--5:145",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-303",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/303",
abstract = "In this paper we study BSDEs with two reflecting
barriers driven by a Brownian motion and an independent
Poisson process. We show the existence and uniqueness
of {\em local\/} and global solutions. As an
application we solve the related zero-sum Dynkin
game.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Backward stochastic differential equation; Dynkin
game; Mokobodzki's condition; Poisson measure",
}
@Article{Song:2006:TSE,
author = "Renming Song",
title = "Two-sided Estimates on the Density of the
{Feynman--Kac} Semigroups of Stable-like Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "6:146--6:161",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-308",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/308",
abstract = "In this paper we establish two-sided estimates for the
density of the Feynman--Kac semigroups of stable-like
processes with potentials given by signed measures
belonging to the Kato class. We also provide similar
estimates for the densities of two other kinds of
Feynman--Kac semigroups of stable-like processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "continuous additive functionals; continuous additive
functionals of zero energy; Feynman--Kac semigroups;
Kato class; purely discontinuous additive functionals.;
Stable processes; stable-like processes",
}
@Article{Tsirelson:2006:BLM,
author = "Boris Tsirelson",
title = "{Brownian} local minima, random dense countable sets
and random equivalence classes",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "7:162--7:198",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-309",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/309",
abstract = "A random dense countable set is characterized (in
distribution) by independence and stationarity. Two
examples are `Brownian local minima' and `unordered
infinite sample'. They are identically distributed. A
framework for such concepts, proposed here, includes a
wide class of random equivalence classes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion; equivalence relation; local minimum;
point process",
}
@Article{Picard:2006:BES,
author = "Jean Picard",
title = "{Brownian} excursions, stochastic integrals, and
representation of {Wiener} functionals",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "8:199--8:248",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-310",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/310",
abstract = "A stochastic calculus similar to Malliavin's calculus
is worked out for Brownian excursions. The analogue of
the Malliavin derivative in this calculus is not a
differential operator, but its adjoint is (like the
Skorohod integral) an extension of the It{\^o}
integral. As an application, we obtain an expression
for the integrand in the stochastic integral
representation of square integrable Wiener functionals;
this expression is an alternative to the classical
Clark--Ocone formula. Moreover, this calculus enables
to construct stochastic integrals of predictable or
anticipating processes (forward, backward and symmetric
integrals are considered).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "anticipating calculus; Brownian excursions; Malliavin
calculus; stochastic integral representation;
stochastic integrals",
}
@Article{Etore:2006:RWS,
author = "Pierre Etor{\'e}",
title = "On random walk simulation of one-dimensional diffusion
processes with discontinuous coefficients",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "9:249--9:275",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-311",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/311",
abstract = "In this paper, we provide a scheme for simulating
one-dimensional processes generated by divergence or
non-divergence form operators with discontinuous
coefficients. We use a space bijection to transform
such a process in another one that behaves locally like
a Skew Brownian motion. Indeed the behavior of the Skew
Brownian motion can easily be approached by an
asymmetric random walk.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Monte Carlo methods, random walk, Skew Brownian
motion, one-dimensional process, divergence form
operator",
}
@Article{Bavouzet:2006:CGU,
author = "Marie Pierre Bavouzet and Marouen Messaoud",
title = "Computation of {Greeks} using {Malliavin}'s calculus
in jump type market models",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "10:276--10:300",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-314",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/314",
abstract = "We use the Malliavin calculus for Poisson processes in
order to compute sensitivities for European and Asian
options with underlying following a jump type
diffusion. The main point is to settle an integration
by parts formula (similar to the one in the Malliavin
calculus) for a general multidimensional random
variable which has an absolutely continuous law with
differentiable density. We give an explicit expression
of the differential operators involved in this formula
and this permits to simulate them and consequently to
run a Monte Carlo algorithm",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Asian options; compound Poisson process; Euler scheme;
European options; Malliavin calculus; Monte-Carlo
algorithm; sensitivity analysis",
}
@Article{Sellke:2006:RRR,
author = "Thomas Sellke",
title = "Recurrence of Reinforced Random Walk on a Ladder",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "11:301--11:310",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-313",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/313",
abstract = "Consider reinforced random walk on a graph that looks
like a doubly infinite ladder. All edges have initial
weight 1, and the reinforcement convention is to add $
\delta > 0 $ to the weight of an edge upon first
crossing, with no reinforcement thereafter. This paper
proves recurrence for all $ \delta > 0 $. In so doing,
we introduce a more general class of processes, termed
multiple-level reinforced random walks.\par
{\bf Editor's Note}. A draft of this paper was written
in 1994. The paper is one of the first to make any
progress on this type of reinforcement problem. It has
motivated a substantial number of new and sometimes
quite difficult studies of reinforcement models in pure
and applied probability. The persistence of interest in
models related to this has caused the original
unpublished manuscript to be frequently cited, despite
its lack of availability and the presence of errors.
The opportunity to rectify this situation has led us to
the somewhat unusual step of publishing a result that
may have already entered the mathematical folklore.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "learning; Markov; martingale; multiple-level;
Reinforced Random Walk",
}
@Article{Grigorescu:2006:TPL,
author = "Ilie Grigorescu and Min Kang",
title = "Tagged Particle Limit for a {Fleming--Viot} Type
System",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "12:311--12:331",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-316",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/316",
abstract = "We consider a branching system of $N$ Brownian
particles evolving independently in a domain $D$ during
any time interval between boundary hits. As soon as one
particle reaches the boundary it is killed and one of
the other particles splits into two independent
particles, the complement of the set $D$ acting as a
catalyst or hard obstacle. Identifying the newly born
particle with the one killed upon contact with the
catalyst, we determine the exact law of the tagged
particle as $N$ approaches infinity. In addition, we
show that any finite number of labelled particles
become independent in the limit. Both results can be
seen as scaling limits of a genome population
undergoing redistribution present in the Fleming--Viot
dynamics.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Fleming--Viot, propagation of chaos, tagged particle",
}
@Article{Deijfen:2006:NCR,
author = "Maria Deijfen and Olle H{\"a}ggstr{\"o}m",
title = "Nonmonotonic Coexistence Regions for the Two-Type
{Richardson} Model on Graphs",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "13:331--13:344",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-321",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/321",
abstract = "In the two-type Richardson model on a graph $ G = (V,
E) $, each vertex is at a given time in state $0$, $1$
or $2$. A $0$ flips to a $1$ (resp.\ $2$) at rate $
\lambda_1$ ($ \lambda_2$) times the number of
neighboring $1$'s ($2$'s), while $1$'s and $2$'s never
flip. When $G$ is infinite, the main question is
whether, starting from a single $1$ and a single $2$,
with positive probability we will see both types of
infection reach infinitely many sites. This has
previously been studied on the $d$-dimensional cubic
lattice $ Z^d$, $ d \geq 2$, where the conjecture (on
which a good deal of progress has been made) is that
such coexistence has positive probability if and only
if $ \lambda_1 = \lambda_2$. In the present paper
examples are given of other graphs where the set of
points in the parameter space which admit such
coexistence has a more surprising form. In particular,
there exist graphs exhibiting coexistence at some value
of $ \frac {\lambda_1}{\lambda_2} \neq 1$ and
non-coexistence when this ratio is brought closer to
$1$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "coexistence; Competing growth; graphs",
}
@Article{Caravenna:2006:SAB,
author = "Francesco Caravenna and Giambattista Giacomin and
Lorenzo Zambotti",
title = "Sharp asymptotic behavior for wetting models in
(1+1)-dimension",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "14:345--14:362",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-320",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/320",
abstract = "We consider continuous and discrete (1+1)-dimensional
wetting models which undergo a
localization/delocalization phase transition. Using a
simple approach based on Renewal Theory we determine
the precise asymptotic behavior of the partition
function, from which we obtain the scaling limits of
the models and an explicit construction of the infinite
volume measure in all regimes, including the critical
one.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Critical Wetting; delta-Pinning Model; Fluctuation
Theory for Random Walks; Renewal Theory; Wetting
Transition",
}
@Article{Limic:2006:SC,
author = "Vlada Limic and Anja Sturm",
title = "The spatial {$ \Lambda $}-coalescent",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "15:363--15:393",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-319",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/319",
abstract = "This paper extends the notion of the $ \Lambda
$-coalescent of Pitman (1999) to the spatial setting.
The partition elements of the spatial $ \Lambda
$-coalescent migrate in a (finite) geographical space
and may only coalesce if located at the same site of
the space. We characterize the $ \Lambda $-coalescents
that come down from infinity, in an analogous way to
Schweinsberg (2000). Surprisingly, all spatial
coalescents that come down from infinity, also come
down from infinity in a uniform way. This enables us to
study space-time asymptotics of spatial $ \Lambda
$-coalescents on large tori in $ d \geq 3$ dimensions.
Some of our results generalize and strengthen the
corresponding results in Greven et al. (2005)
concerning the spatial Kingman coalescent.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "$la$-coalescent; coalescent; limit theorems,
coalescing random walks; structured coalescent",
}
@Article{Basdevant:2006:FOP,
author = "Anne-Laure Basdevant",
title = "Fragmentation of Ordered Partitions and Intervals",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "16:394--16:417",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-323",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/323",
abstract = "Fragmentation processes of exchangeable partitions
have already been studied by several authors. This
paper deals with fragmentations of exchangeable
compositions, i.e., partitions of $ \mathbb {N} $ in
which the order of the blocks matters. We will prove
that such a fragmentation is bijectively associated to
an interval fragmentation. Using this correspondence,
we then study two examples: Ruelle's interval
fragmentation and the interval fragmentation derived
from the standard additive coalescent.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "exchangeable compositions; Interval fragmentation",
}
@Article{Holroyd:2006:MTM,
author = "Alexander Holroyd",
title = "The Metastability Threshold for Modified Bootstrap
Percolation in $d$ Dimensions",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "17:418--17:433",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-326",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/326",
abstract = "In the modified bootstrap percolation model, sites in
the cube $ \{ 1, \ldots, L \}^d $ are initially
declared active independently with probability $p$. At
subsequent steps, an inactive site becomes active if it
has at least one active nearest neighbour in each of
the $d$ dimensions, while an active site remains active
forever. We study the probability that the entire cube
is eventually active. For all $ d \geq 2$ we prove that
as $ L \to \infty $ and $ p \to 0$ simultaneously, this
probability converges to $1$ if $ L \geq \exp \cdots
\exp \frac {\lambda + \epsilon }{p}$, and converges to
$0$ if $ L \leq \exp \cdots \exp \frac {\lambda -
\epsilon }{p}$, for any $ \epsilon > 0$. Here the
exponential function is iterated $ d - 1$ times, and
the threshold $ \lambda $ equals $ \pi^2 / 6$ for all
$d$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "bootstrap percolation; cellular automaton; finite-size
scaling; metastability",
}
@Article{Nane:2006:LIL,
author = "Erkan Nane",
title = "Laws of the iterated logarithm for $ \alpha $-time
{Brownian} motion",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "18:434--18:459",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-327",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/327",
abstract = "We introduce a class of iterated processes called $
\alpha $-time Brownian motion for $ 0 < \alpha \leq 2$.
These are obtained by taking Brownian motion and
replacing the time parameter with a symmetric $ \alpha
$-stable process. We prove a Chung-type law of the
iterated logarithm (LIL) for these processes which is a
generalization of LIL proved in {citehu} for iterated
Brownian motion. When $ \alpha = 1$ it takes the
following form\par
$$ \liminf_{T \to \infty } \ T^{-1 / 2}(\log \log T)
\sup_{0 \leq t \leq T}|Z_t| = \pi^2 \sqrt {\lambda_1}
\quad a.s. $$
where $ \lambda_1$ is the first eigenvalue for the
Cauchy process in the interval $ [ - 1, 1].$ We also
define the local time $ L^*(x, t)$ and range $ R^*(t) =
|{x \colon Z(s) = x \text { for some } s \leq t}|$ for
these processes for $ 1 < \alpha < 2$. We prove that
there are universal constants $ c_R, c_L \in (0,
\infty) $ such that\par
$$ \limsup_{t \to \infty } \frac {R^*(t)}{(t / \log
\log t)^{1 / 2 \alpha } \log \log t} = c_R \quad a.s.
$$
$$ \liminf_{t \to \infty } \frac {\sup_{x \in
{R}}L^*(x, t)}{(t / \log \log t)^{1 - 1 / 2 \alpha }} =
c_L \quad a.s. $$",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion, symmetric $alpha$-stable process,
$alpha$-time Brownian motion, local time, Chung's law,
Kesten's law",
}
@Article{Adams:2006:LSP,
author = "Stefan Adams and Jean-Bernard Bru and Wolfgang
Koenig",
title = "Large systems of path-repellent {Brownian} motions in
a trap at positive temperature",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "19:460--19:485",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-330",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/330",
abstract = "We study a model of $N$ mutually repellent Brownian
motions under confinement to stay in some bounded
region of space. Our model is defined in terms of a
transformed path measure under a trap Hamiltonian,
which prevents the motions from escaping to infinity,
and a pair-interaction Hamiltonian, which imposes a
repellency of the $N$ paths. In fact, this interaction
is an $N$-dependent regularisation of the Brownian
intersection local times, an object which is of
independent interest in the theory of stochastic
processes. The time horizon (interpreted as the inverse
temperature) is kept fixed. We analyse the model for
diverging number of Brownian motions in terms of a
large deviation principle. The resulting variational
formula is the positive-temperature analogue of the
well-known Gross--Pitaevskii formula, which
approximates the ground state of a certain dilute large
quantum system; the kinetic energy term of that formula
is replaced by a probabilistic energy functional. This
study is a continuation of the analysis in [ABK06]
where we considered the limit of diverging time (i.e.,
the zero-temperature limit) with fixed number of
Brownian motions, followed by the limit for diverging
number of motions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian intersection local times; Gross--Pitaevskii
formula; Interacting Brownian motions; large
deviations; occupation measure",
}
@Article{Klein:2006:CCI,
author = "Thierry Klein and Yutao Ma and Nicolas Privault",
title = "Convex Concentration Inequalities and
Forward--Backward Stochastic Calculus",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "20:486--20:512",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-332",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/332",
abstract = "Given $ (M_t)_{t \in \mathbb {R}_+} $ and $ (M^*_t)_{t
\in \mathbb {R}_+} $ respectively a forward and a
backward martingale with jumps and continuous parts, we
prove that $ E[\phi (M_t + M^*_t)] $ is non-increasing
in $t$ when $ \phi $ is a convex function, provided the
local characteristics of $ (M_t)_{t \in \mathbb {R}_+}$
and $ (M^*_t)_{t \in \mathbb {R}_+}$ satisfy some
comparison inequalities. We deduce convex concentration
inequalities and deviation bounds for random variables
admitting a predictable representation in terms of a
Brownian motion and a non-necessarily independent jump
component",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Convex concentration inequalities, forward--backward
stochastic calculus, deviation inequalities, Clark
formula, Brownian motion, jump processes",
}
@Article{Maximilian:2006:EMD,
author = "Duerre Maximilian",
title = "Existence of multi-dimensional infinite volume
self-organized critical forest-fire models",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "21:513--21:539",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-333",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/333",
abstract = "Consider the following forest-fire model where the
possible locations of trees are the sites of a cubic
lattice. Each site has two possible states: 'vacant' or
'occupied'. Vacant sites become occupied according to
independent rate 1 Poisson processes. Independently, at
each site ignition (by lightning) occurs according to
independent rate lambda Poisson processes. When a site
is ignited, its occupied cluster becomes vacant
instantaneously. If the lattice is one-dimensional or
finite, then with probability one, at each time the
state of a given site only depends on finitely many
Poisson events; a process with the above description
can be constructed in a standard way. If the lattice is
infinite and multi-dimensional, in principle, the state
of a given site can be influenced by infinitely many
Poisson events in finite time.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "existence; forest-fire model; forest-fires;
self-organized criticality; well-defined",
}
@Article{Schmitz:2006:ECD,
author = "Tom Schmitz",
title = "Examples of Condition {$ (T) $} for Diffusions in a
Random Environment",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "22:540--22:562",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-337",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/337",
abstract = "With the help of the methods developed in our previous
article [Schmitz, to appear in Annales de l'I.H.P., in
press], we highlight condition $ (T) $ as a source of
new examples of 'ballistic' diffusions in a random
environment when $ d > 1 $ ('ballistic' means that a
strong law of large numbers with non-vanishing limiting
velocity holds). In particular we are able to treat the
case of non-constant diffusion coefficients, a feature
that causes problems. Further we recover the ballistic
character of two important classes of diffusions in a
random environment by simply checking condition $ (T)
$. This not only points out to the broad range of
examples where condition $ (T) $ can be checked, but
also fortifies our belief that condition $ (T) $ is a
natural contender for the characterisation of ballistic
diffusions in a random environment when $ d > 1 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Diffusions in a random environment, ballistic
behavior, Condition $(T)$",
}
@Article{Kim:2006:PSD,
author = "Kyeong-Hun Kim",
title = "Parabolic {SPDEs} Degenerating on the Boundary of
Non-Smooth Domain",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "23:563--23:584",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-339",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/339",
abstract = "Degenerate stochastic partial differential equations
of divergence and non-divergence forms are considered
in non-smooth domains. Existence and uniqueness results
are given in weighted Sobolev spaces, and Holder
estimates of the solutions are presented.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "SPDEs degenerating on the boundary; weighted Sobolev
spaces",
}
@Article{Swart:2006:RAC,
author = "Jan Swart and Klaus Fleischmann",
title = "Renormalization analysis of catalytic {Wright--Fisher}
diffusions",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "24:585--24:654",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-341",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/341",
abstract = "Recently, several authors have studied maps where a
function, describing the local diffusion matrix of a
diffusion process with a linear drift towards an
attraction point, is mapped into the average of that
function with respect to the unique invariant measure
of the diffusion process, as a function of the
attraction point. Such mappings arise in the analysis
of infinite systems of diffusions indexed by the
hierarchical group, with a linear attractive
interaction between the components. In this context,
the mappings are called renormalization
transformations. We consider such maps for catalytic
Wright--Fisher diffusions. These are diffusions on the
unit square where the first component (the catalyst)
performs an autonomous Wright--Fisher diffusion, while
the second component (the reactant) performs a
Wright--Fisher diffusion with a rate depending on the
first component through a catalyzing function. We
determine the limit of rescaled iterates of
renormalization transformations acting on the diffusion
matrices of such catalytic Wright--Fisher diffusions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Renormalization, catalytic Wright--Fisher diffusion,
embedded particle system, extinction, unbounded growth,
interacting diffusions, universality",
}
@Article{Berger:2006:TPC,
author = "Noam Berger and Itai Benjamini and Omer Angel and
Yuval Peres",
title = "Transience of percolation clusters on wedges",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "25:655--25:669",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-345",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/345",
abstract = "We study random walks on supercritical percolation
clusters on wedges in $ Z^3 $, and show that the
infinite percolation cluster is (a.s.) transient
whenever the wedge is transient. This solves a question
raised by O. H{\"a}ggstr{\"o}m and E. Mossel. We also
show that for convex gauge functions satisfying a mild
regularity condition, the existence of a finite energy
flow on $ Z^2 $ is equivalent to the (a.s.) existence
of a finite energy flow on the supercritical
percolation cluster. This answers a question of C.
Hoffman.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "percolation; transience; wedges",
}
@Article{Cator:2006:BSC,
author = "Eric Cator and Sergei Dobrynin",
title = "Behavior of a second class particle in {Hammersley}'s
process",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "26:670--26:685",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-340",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/340",
abstract = "In the case of a rarefaction fan in a non-stationary
Hammersley process, we explicitly calculate the
asymptotic behavior of the process as we move out along
a ray, and the asymptotic distribution of the angle
within the rarefaction fan of a second class particle
and a dual second class particle. Furthermore, we
consider a stationary Hammersley process and use the
previous results to show that trajectories of a second
class particle and a dual second class particles touch
with probability one, and we give some information on
the area enclosed by the two trajectories, up until the
first intersection point. This is linked to the area of
influence of an added Poisson point in the plane.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Hammersley's process; rarefaction fan; second class
particles",
}
@Article{Odasso:2006:SSS,
author = "Cyril Odasso",
title = "Spatial Smoothness of the Stationary Solutions of the
{$3$D} {Navier--Stokes} Equations",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "27:686--27:699",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-336",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/336",
abstract = "We consider stationary solutions of the three
dimensional Navier--Stokes equations (NS3D) with
periodic boundary conditions and driven by an external
force which might have a deterministic and a random
part. The random part of the force is white in time and
very smooth in space. We investigate smoothness
properties in space of the stationary solutions.
Classical technics for studying smoothness of
stochastic PDEs do not seem to apply since global
existence of strong solutions is not known. We use the
Kolmogorov operator and Galerkin approximations. We
first assume that the noise has spatial regularity of
order $p$ in the $ L^2$ based Sobolev spaces, in other
words that its paths are in $ H^p$. Then we prove that
at each fixed time the law of the stationary solutions
is supported by $ H^{p + 1}$. Then, using a totally
different technic, we prove that if the noise has
Gevrey regularity then at each fixed time, the law of a
stationary solution is supported by a Gevrey space.
Some information on the Kolmogorov dissipation scale is
deduced.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic three-dimensional Navier--Stokes equations,
invariant measure",
}
@Article{Dereich:2006:HRQ,
author = "Steffen Dereich and Michael Scheutzow",
title = "High Resolution Quantization and Entropy Coding for
Fractional {Brownian} Motion",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "28:700--28:722",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-344",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/344",
abstract = "We establish the precise asymptotics of the
quantization and entropy coding errors for fractional
Brownian motion with respect to the supremum norm and $
L^p [0, 1]$-norm distortions. We show that all moments
in the quantization problem lead to the same
asymptotics. Using a general principle, we conclude
that entropy coding and quantization coincide
asymptotically. Under supremum-norm distortion, our
proof uses an explicit construction of efficient
codebooks based on a particular entropy constrained
coding scheme.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "complexity; distortion rate function; entropy;
High-resolution quantization; stochastic process",
}
@Article{Fleischmann:2006:HLF,
author = "Klaus Fleischmann and Peter M{\"o}rters and Vitali
Wachtel",
title = "Hydrodynamic Limit Fluctuations of Super-{Brownian}
Motion with a Stable Catalyst",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "29:723--29:767",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-348",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/348",
abstract = "We consider the behaviour of a continuous
super-Brownian motion catalysed by a random medium with
infinite overall density under the hydrodynamic scaling
of mass, time, and space. We show that, in
supercritical dimensions, the scaled process converges
to a macroscopic heat flow, and the appropriately
rescaled random fluctuations around this macroscopic
flow are asymptotically bounded, in the sense of
log-Laplace transforms, by generalised stable
Ornstein--Uhlenbeck processes. The most interesting new
effect we observe is the occurrence of an index-jump
from a Gaussian situation to stable fluctuations of
index $ 1 + \gamma $, where $ \gamma \in (0, 1) $ is an
index associated to the medium.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Catalyst, reactant, superprocess, critical scaling,
refined law of large numbers, catalytic branching,
stable medium, random environment, supercritical
dimension, generalised stable Ornstein--Uhlenbeck
process, index jump, parabolic Anderson model with
sta",
}
@Article{Belhaouari:2006:CRS,
author = "Samir Belhaouari and Thomas Mountford and Rongfeng Sun
and Glauco Valle",
title = "Convergence Results and Sharp Estimates for the Voter
Model Interfaces",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "30:768--30:801",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-349",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/349",
abstract = "We study the evolution of the interface for the
one-dimensional voter model. We show that if the random
walk kernel associated with the voter model has finite
$ \gamma $-th moment for some $ \gamma > 3$, then the
evolution of the interface boundaries converge weakly
to a Brownian motion under diffusive scaling. This
extends recent work of Newman, Ravishankar and Sun. Our
result is optimal in the sense that finite $ \gamma
$-th moment is necessary for this convergence for all $
\gamma \in (0, 3)$. We also obtain relatively sharp
estimates for the tail distribution of the size of the
equilibrium interface, extending earlier results of Cox
and Durrett, and Belhaouari, Mountford and Valle.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "voter model interface, coalescing random walks,
Brownian web, invariance principle",
}
@Article{Sabot:2006:RWD,
author = "Christophe Sabot and Nathana{\"e}l Enriquez",
title = "Random Walks in a {Dirichlet} Environment",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "31:802--31:816",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-350",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/350",
abstract = "This paper states a law of large numbers for a random
walk in a random iid environment on $ Z^d $, where the
environment follows some Dirichlet distribution.
Moreover, we give explicit bounds for the asymptotic
velocity of the process and also an asymptotic
expansion of this velocity at low disorder.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Random Walks, Random Environments, Dirichlet Laws,
Reinforced Random Walks",
}
@Article{Xiao:2006:SLN,
author = "Yimin Xiao and Davar Khoshnevisan and Dongsheng Wu",
title = "Sectorial Local Non-Determinism and the Geometry of
the {Brownian} Sheet",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "32:817--32:843",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-353",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/353",
abstract = "We prove the following results about the images and
multiple points of an $N$-parameter, $d$-dimensional
Brownian sheet $ B = \{ B(t) \}_{t \in R_+^N}$:
(1) If $ \text {dim}_H F \leq d / 2$, then $ B(F)$ is
almost surely a Salem set.\par
(2) If $ N \leq d / 2$, then with probability one $
\text {dim}_H B(F) = 2 \text {dim} F$ for all Borel
sets of $ R_+^N$, where ``$ \text {dim}_H$'' could be
everywhere replaced by the ``Hausdorff, '' ``packing,
'' ``upper Minkowski, '' or ``lower Minkowski
dimension.''\par
(3) Let $ M_k$ be the set of $k$-multiple points of
$B$. If $ N \leq d / 2$ and $ N k > (k - 1)d / 2$, then
$ \text {dim}_H M_k = \text {dim}_p M_k = 2 N k - (k -
1)d$, a.s.\par
The Hausdorff dimension aspect of (2) was proved
earlier; see Mountford (1989) and Lin (1999). The
latter references use two different methods; ours of
(2) are more elementary, and reminiscent of the earlier
arguments of Monrad and Pitt (1987) that were designed
for studying fractional Brownian motion. If $ N > d /
2$ then (2) fails to hold. In that case, we establish
uniform-dimensional properties for the $ (N,
1)$-Brownian sheet that extend the results of Kaufman
(1989) for 1-dimensional Brownian motion. Our
innovation is in our use of the {\em sectorial local
nondeterminism} of the Brownian sheet (Khoshnevisan and
Xiao, 2004).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian sheet, sectorial local nondeterminism, image,
Salem sets, multiple points, Hausdorff dimension,
packing dimension",
}
@Article{Dony:2006:WUC,
author = "Julia Dony and Uwe Einmahl",
title = "Weighted uniform consistency of kernel density
estimators with general bandwidth sequences",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "33:844--33:859",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-354",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/354",
abstract = "Let $ f_{n, h} $ be a kernel density estimator of a
continuous and bounded $d$-dimensional density $f$. Let
$ \psi (t)$ be a positive continuous function such that
$ \| \psi f^\beta \|_\infty < \infty $ for some $ 0 <
\beta < 1 / 2$. We are interested in the rate of
consistency of such estimators with respect to the
weighted sup-norm determined by $ \psi $. This problem
has been considered by Gin, Koltchinskii and Zinn
(2004) for a deterministic bandwidth $ h_n$. We provide
``uniform in $h$'' versions of some of their results,
allowing us to determine the corresponding rates of
consistency for kernel density estimators where the
bandwidth sequences may depend on the data and/or the
location.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "convergence rates; empirical process; kernel density
estimator; uniform in bandwidth; weighted uniform
consistency",
}
@Article{Feyel:2006:CIA,
author = "Denis Feyel and Arnaud {de La Pradelle}",
title = "Curvilinear Integrals Along Enriched Paths",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "34:860--34:892",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-356",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/356",
abstract = "Inspired by the fundamental work of T. J. Lyons, we
develop a theory of curvilinear integrals along a new
kind of enriched paths in $ R^d $. We apply these
methods to the fractional Brownian Motion, and prove a
support theorem for SDE driven by the Skorohod fBM of
Hurst parameter $ H > 1 / 4 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Curvilinear integrals, H{\"o}lder continuity, rough
paths, stochastic integrals, stochastic differential
equations, fractional Brownian motion.",
}
@Article{Wagner:2006:PGB,
author = "Wolfgang Wagner",
title = "Post-gelation behavior of a spatial coagulation
model",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "35:893--35:933",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-359",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/359",
abstract = "A coagulation model on a finite spatial grid is
considered. Particles of discrete masses jump randomly
between sites and, while located at the same site,
stick together according to some coagulation kernel.
The asymptotic behavior (for increasing particle
numbers) of this model is studied in the situation when
the coagulation kernel grows sufficiently fast so that
the phenomenon of gelation is observed. Weak
accumulation points of an appropriate sequence of
measure-valued processes are characterized in terms of
solutions of a nonlinear equation. A natural
description of the behavior of the gel is obtained by
using the one-point compactification of the size space.
Two aspects of the limiting equation are of special
interest. First, for a certain class of coagulation
kernels, this equation differs from a naive extension
of Smoluchowski's coagulation equation. Second, due to
spatial inhomogeneity, an equation for the time
evolution of the gel mass density has to be added. The
jump rates are assumed to vanish with increasing
particle masses so that the gel is immobile. Two
different gel growth mechanisms (active and passive
gel) are found depending on the type of the coagulation
kernel.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "post-gelation behavior; Spatial coagulation model;
stochastic particle systems",
}
@Article{Ramanan:2006:RDD,
author = "Kavita Ramanan",
title = "Reflected Diffusions Defined via the Extended
{Skorokhod} Map",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "36:934--36:992",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-360",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/360",
abstract = "This work introduces the extended Skorokhod problem
(ESP) and associated extended Skorokhod map (ESM) that
enable a pathwise construction of reflected diffusions
that are not necessarily semimartingales. Roughly
speaking, given the closure $G$ of an open connected
set in $ {\mathbb R}^J$, a non-empty convex cone $ d(x)
\subset {\mathbb R}^J$ specified at each point $x$ on
the boundary $ \partial G$, and a c{\`a}dl{\`a}g
trajectory $ \psi $ taking values in $ {\mathbb R}^J$,
the ESM $ \bar \Gamma $ defines a constrained version $
\phi $ of $ \psi $ that takes values in $G$ and is such
that the increments of $ \phi - \psi $ on any interval
$ [s, t]$ lie in the closed convex hull of the
directions $ d(\phi (u)), u \in (s, t]$. When the graph
of $ d(\cdot)$ is closed, the following three
properties are established: (i) given $ \psi $, if $
(\phi, \eta)$ solve the ESP then $ (\phi, \eta)$ solve
the corresponding Skorokhod problem (SP) if and only if
$ \eta $ is of bounded variation; (ii) given $ \psi $,
any solution $ (\phi, \eta)$ to the ESP is a solution
to the SP on the interval $ [0, \tau_0)$, but not in
general on $ [0, \tau_0]$, where $ \tau_0$ is the first
time that $ \phi $ hits the set $ {\cal V}$ of points $
x \in \partial G$ such that $ d(x)$ contains a line;
(iii) the graph of the ESM $ \bar \Gamma $ is closed on
the space of c{\`a}dl{\`a}g trajectories (with respect
to both the uniform and the $ J_1$-Skorokhod
topologies).\par
The paper then focuses on a class of multi-dimensional
ESPs on polyhedral domains with a non-empty $ {\cal
V}$-set. Uniqueness and existence of solutions for this
class of ESPs is established and existence and pathwise
uniqueness of strong solutions to the associated
stochastic differential equations with reflection is
derived. The associated reflected diffusions are also
shown to satisfy the corresponding submartingale
problem. Lastly, it is proved that these reflected
diffusions are semimartingales on $ [0, \tau_0]$. One
motivation for the study of this class of reflected
diffusions is that they arise as approximations of
queueing networks in heavy traffic that use the
so-called generalised processor sharing discipline.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "reflected diffusions; Skorokhod problem; stochastic
differential equations; submartingale problem",
}
@Article{Bass:2006:MDL,
author = "Richard Bass and Xia Chen and Jay Rosen",
title = "Moderate deviations and laws of the iterated logarithm
for the renormalized self-intersection local times of
planar random walks",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "37:993--37:1030",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-362",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/362",
abstract = "We study moderate deviations for the renormalized
self-intersection local time of planar random walks. We
also prove laws of the iterated logarithm for such
local times.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion; Gagliardo--Nirenberg; intersection
local time; large deviations; law of the iterated
logarithm; moderate deviations; planar random walks",
}
@Article{Gapeev:2006:DOS,
author = "Pavel Gapeev",
title = "Discounted optimal stopping for maxima in diffusion
models with finite horizon",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "38:1031--38:1048",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-367",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/367",
abstract = "We present a solution to some discounted optimal
stopping problem for the maximum of a geometric
Brownian motion on a finite time interval. The method
of proof is based on reducing the initial optimal
stopping problem with the continuation region
determined by an increasing continuous boundary surface
to a parabolic free-boundary problem. Using the
change-of-variable formula with local time on surfaces
we show that the optimal boundary can be characterized
as a unique solution of a nonlinear integral equation.
The result can be interpreted as pricing American
fixed-strike lookback option in a diffusion model with
finite time horizon.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "a change-of-varia; a nonlinear Volterra integral
equation of the second kind; boundary surface;
Discounted optimal stopping problem; finite horizon;
geometric Brownian motion; maximum process; normal
reflection; parabolic free-boundary problem; smooth
fit",
}
@Article{Pinelis:2006:NDS,
author = "Iosif Pinelis",
title = "On normal domination of (super)martingales",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "39:1049--39:1070",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-371",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/371",
abstract = "Let $ (S_0, S_1, \dots) $ be a supermartingale
relative to a nondecreasing sequence of $ \sigma
$-algebras $ (H_{\le 0}, H_{\le 1}, \dots)$, with $ S_0
\leq 0$ almost surely (a.s.) and differences $ X_i :=
S_i - S_{i - 1}$. Suppose that for every $ i = 1, 2,
\dots $ there exist $ H_{\le (i - 1)}$-measurable
r.v.'s $ C_{i - 1}$ and $ D_{i - 1}$ and a positive
real number $ s_i$ such that $ C_{i - 1} \leq X_i \le
D_{i - 1}$ and $ D_{i - 1} - C_{i - 1} \leq 2 s_i$ a.s.
Then for all real $t$ and natural $n$ and all functions
$f$ satisfying certain convexity conditions $ E f(S_n)
\leq E f(s Z)$, where $ f_t(x) := \max (0, x - t)^5$, $
s := \sqrt {s_1^2 + \dots + s_n^2}$, and $ Z \sim N(0,
1)$. In particular, this implies $ P(S_n \ge x) \le
c_{5, 0}P(s Z \ge x) \quad \forall x \in R$, where $
c_{5, 0} = 5 !(e / 5)^5 = 5.699 \dots $. Results for $
\max_{0 \leq k \leq n}S_k$ in place of $ S_n$ and for
concentration of measure also follow.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "generalized moments; martingales; probability
inequalities; supermartingales; upper bounds",
}
@Article{Chazottes:2006:REW,
author = "Jean-Ren{\'e} Chazottes and Cristian Giardina and
Frank Redig",
title = "Relative entropy and waiting times for continuous-time
{Markov} processes",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "40:1049--40:1068",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-374",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/374",
abstract = "For discrete-time stochastic processes, there is a
close connection between return (resp. waiting) times
and entropy (resp. relative entropy). Such a connection
cannot be straightforwardly extended to the
continuous-time setting. Contrarily to the
discrete-time case one needs a reference measure on
path space and so the natural object is relative
entropy rather than entropy. In this paper we elaborate
on this in the case of continuous-time Markov processes
with finite state space. A reference measure of special
interest is the one associated to the time-reversed
process. In that case relative entropy is interpreted
as the entropy production rate. The main results of
this paper are: almost-sure convergence to relative
entropy of the logarithm of waiting-times ratios
suitably normalized, and their fluctuation properties
(central limit theorem and large deviation
principle).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "continuous-time Markov chain, law of large numbers,
central limit theorem, large deviations, entropy
production, time-reversed process",
}
@Article{Zhan:2006:SPA,
author = "Dapeng Zhan",
title = "Some Properties of Annulus {SLE}",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "41:1069--41:1093",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-338",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/338",
abstract = "An annulus SLE$_\kappa $ trace tends to a single point
on the target circle, and the density function of the
end point satisfies some differential equation. Some
martingales or local martingales are found for annulus
SLE$_4$, SLE$_8$ and SLE$_8 / 3$. From the local
martingale for annulus SLE$_4$ we find a candidate of
discrete lattice model that may have annulus SLE$_4$ as
its scaling limit. The local martingale for annulus
SLE$_8 / 3$ is similar to those for chordal and radial
SLE$_8 / 3$. But it seems that annulus SLE$_8 / 3$ does
not satisfy the restriction property",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "continuum scaling limit, percolation, SLE, conformal
invariance",
}
@Article{Balazs:2006:CRF,
author = "Marton Balazs and Eric Cator and Timo Seppalainen",
title = "Cube Root Fluctuations for the Corner Growth Model
Associated to the Exclusion Process",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "42:1094--42:1132",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-366",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/366",
abstract = "We study the last-passage growth model on the planar
integer lattice with exponential weights. With boundary
conditions that represent the equilibrium exclusion
process as seen from a particle right after its jump we
prove that the variance of the last-passage time in a
characteristic direction is of order $ t^{2 / 3} $.
With more general boundary conditions that include the
rarefaction fan case we show that the last-passage time
fluctuations are still of order $ t^{1 / 3} $, and also
that the transversal fluctuations of the maximal path
have order $ t^{2 / 3} $. We adapt and then build on a
recent study of Hammersley's process by Cator and
Groeneboom, and also utilize the competition interface
introduced by Ferrari, Martin and Pimentel. The
arguments are entirely probabilistic, and no use is
made of the combinatorics of Young tableaux or methods
of asymptotic analysis.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Burke's theorem; competition interface; cube root
asymptotics; Last-passage; rarefaction fan; simple
exclusion",
}
@Article{Brouwer:2006:CSD,
author = "Rachel Brouwer and Juho Pennanen",
title = "The Cluster Size Distribution for a Forest-Fire
Process on {$Z$}",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "43:1133--43:1143",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-369",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/369",
abstract = "Consider the following forest-fire model where trees
are located on sites of $ \mathbb {Z} $. A site can be
vacant or be occupied by a tree. Each vacant site
becomes occupied at rate $1$, independently of the
other sites. Each site is hit by lightning with rate $
\lambda $, which burns down the occupied cluster of
that site instantaneously. As $ \lambda \downarrow 0$
this process is believed to display self-organised
critical behaviour.\par
This paper is mainly concerned with the cluster size
distribution in steady-state. Drossel, Clar and Schwabl
(1993) claimed that the cluster size distribution has a
certain power law behaviour which holds for cluster
sizes that are not too large compared to some explicit
cluster size $ s_{max}$. The latter can be written in
terms of $ \lambda $ approximately as $ s_{max} \ln
(s_{max}) = 1 / \lambda $. However, Van den Berg and
Jarai (2005) showed that this claim is not correct for
cluster sizes of order $ s_{max}$, which left the
question for which cluster sizes the power law
behaviour {\em does} hold. Our main result is a
rigorous proof of the power law behaviour up to cluster
sizes of the order $ s_{max}^{1 / 3}$. Further, it
proves the existence of a stationary translation
invariant distribution, which was always assumed but
never shown rigorously in the literature.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "forest-fires, self-organised criticality, cluster size
distribution",
}
@Article{Shiga:2006:IDR,
author = "Tokuzo Shiga and Hiroshi Tanaka",
title = "Infinitely Divisible Random Probability Distributions
with an Application to a Random Motion in a Random
Environment",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "44:1144--44:1183",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-380",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/380",
abstract = "The infinite divisibility of probability distributions
on the space $ P (R) $ of probability distributions on
$R$ is defined and related fundamental results such as
the L{\'e}vy--Khintchin formula, representation of
It{\^o} type of infinitely divisible RPD, stable RPD
and Levy processes on $ P (R)$ are obtained. As an
application we investigate limiting behaviors of a
simple model of a particle motion in a random
environment",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "infinite divisibility; L{\'e}vy-It{\^o}
repr{\'e}sentation; L{\'e}vy-Khintchin representation;
random environment; random probability distribution",
}
@Article{Bertacchi:2006:ABS,
author = "Daniela Bertacchi",
title = "Asymptotic Behaviour of the Simple Random Walk on the
$2$-dimensional Comb",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "45:1184--45:1203",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-377",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/377",
abstract = "We analyze the differences between the horizontal and
the vertical component of the simple random walk on the
2-dimensional comb. In particular we evaluate by
combinatorial methods the asymptotic behaviour of the
expected value of the distance from the origin, the
maximal deviation and the maximal span in $n$ steps,
proving that for all these quantities the order is $
n^{1 / 4}$ for the horizontal projection and $ n^{1 /
2}$ for the vertical one (the exact constants are
determined). Then we rescale the two projections of the
random walk dividing by $ n^{1 / 4}$ and $ n^{1 / 2}$
the horizontal and vertical ones, respectively. The
limit process is obtained. With similar techniques the
walk dimension is determined, showing that the Einstein
relation between the fractal, spectral and walk
dimensions does not hold on the comb.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian Motion; Comb; Generating Function; Maximal
Excursion; Random Walk",
}
@Article{Lifshits:2006:SDG,
author = "Mikhail Lifshits and Werner Linde and Zhan Shi",
title = "Small Deviations of {Gaussian} Random Fields in {$ L_q
$}-Spaces",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "46:1204--46:1233",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-379",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/379",
abstract = "We investigate small deviation properties of Gaussian
random fields in the space $ L_q(R^N, \mu) $ where $
\mu $ is an arbitrary finite compactly supported Borel
measure. Of special interest are hereby ``thin''
measures $ \mu $, i.e., those which are singular with
respect to the $N$--dimensional Lebesgue measure; the
so-called self-similar measures providing a class of
typical examples. For a large class of random fields
(including, among others, fractional Brownian motions),
we describe the behavior of small deviation
probabilities via numerical characteristics of $ \mu $,
called mixed entropy, characterizing size and
regularity of $ \mu $. For the particularly interesting
case of self-similar measures $ \mu $, the asymptotic
behavior of the mixed entropy is evaluated explicitly.
As a consequence, we get the asymptotic of the small
deviation for $N$-parameter fractional Brownian motions
with respect to $ L_q(R^N, \mu)$-norms. While the upper
estimates for the small deviation probabilities are
proved by purely probabilistic methods, the lower
bounds are established by analytic tools concerning
Kolmogorov and entropy numbers of Holder operators.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "fractal measures; fractional Brownian motion; Gaussian
random fields; Kolmogorov numbers; metric entropy",
}
@Article{Barbour:2006:DSW,
author = "Andrew Barbour and Gesine Reinert",
title = "Discrete small world networks",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "47:1234--47:1283",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-381",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/381",
abstract = "Small world models are networks consisting of many
local links and fewer long range `shortcuts', used to
model networks with a high degree of local clustering
but relatively small diameter. Here, we concern
ourselves with the distribution of typical inter-point
network distances. We establish approximations to the
distribution of the graph distance in a discrete ring
network with extra random links, and compare the
results to those for simpler models, in which the extra
links have zero length and the ring is continuous.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Small-world networks, shortest path length, branching
process",
}
@Article{Su:2006:GFC,
author = "Zhonggen Su",
title = "{Gaussian} Fluctuations in Complex Sample Covariance
Matrices",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "48:1284--48:1320",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-378",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/378",
abstract = "Let $ X = (X_{i, j})_{m \times n}, m \ge n $, be a
complex Gaussian random matrix with mean zero and
variance $ \frac 1 n $, let $ S = X^*X $ be a sample
covariance matrix. In this paper we are mainly
interested in the limiting behavior of eigenvalues when
$ \frac m n \rightarrow \gamma \ge 1 $ as $ n
\rightarrow \infty $. Under certain conditions on $k$,
we prove the central limit theorem holds true for the
$k$-th largest eigenvalues $ \lambda_{(k)}$ as $k$
tends to infinity as $ n \rightarrow \infty $. The
proof is largely based on the
Costin--Lebowitz--Soshnikov argument and the asymptotic
estimates for the expectation and variance of the
number of eigenvalues in an interval. The standard
technique for the RH problem is used to compute the
exact formula and asymptotic properties for the mean
density of eigenvalues. As a by-product, we obtain a
convergence speed of the mean density of eigenvalues to
the Marchenko--Pastur distribution density under the
condition $ | \frac m n - \gamma | = O(\frac 1 n)$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Central limit theorem; Eigenvalues; RH problems;
Sample covariance matrices; the
Costin--Lebowitz--Soshnikov theorem",
}
@Article{Chaumont:2006:LEP,
author = "Loic Chaumont and Juan Carlos Pardo Millan",
title = "The Lower Envelope of Positive Self-Similar {Markov}
Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "49:1321--49:1341",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-382",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/382",
abstract = "We establish integral tests and laws of the iterated
logarithm for the lower envelope of positive
self-similar Markov processes at 0 and $ + \infty $.
Our proofs are based on the Lamperti representation and
time reversal arguments. These results extend laws of
the iterated logarithm for Bessel processes due to
Dvoretzky and Erdos (1951), Motoo (1958), and Rivero
(2003).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Self-similar Markov process, L'evy process, Lamperti
representation, last passage time, time reversal,
integral test, law of the iterated logarithm",
}
@Article{Johansson:2006:EGM,
author = "Kurt Johansson and Eric Nordenstam",
title = "Eigenvalues of {GUE} Minors",
journal = j-ELECTRON-J-PROBAB,
volume = "11",
pages = "50:1342--50:1371",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v11-370",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
note = "See erratum \cite{Johansson:2007:EEG}.",
URL = "http://ejp.ejpecp.org/article/view/370",
abstract = "Consider an infinite random matrix $ H = (h_{ij})_{0 <
i, j} $ picked from the Gaussian Unitary Ensemble
(GUE). Denote its main minors by $ H_i = (h_{rs})_{1
\leq r, s \leq i} $ and let the $j$:th largest
eigenvalue of $ H_i$ be $ \mu^i_j$. We show that the
configuration of all these eigenvalues $ (i, \mu_j^i)$
form a determinantal point process on $ \mathbb {N}
\times \mathbb {R}$.\par
Furthermore we show that this process can be obtained
as the scaling limit in random tilings of the Aztec
diamond close to the boundary. We also discuss the
corresponding limit for random lozenge tilings of a
hexagon.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Random matrices; Tiling problems",
}
@Article{Bass:2007:FPR,
author = "Richard Bass and Jay Rosen",
title = "Frequent Points for Random Walks in Two Dimensions",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "1:1--1:46",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-388",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/388",
abstract = "For a symmetric random walk in $ Z^2 $ which does not
necessarily have bounded jumps we study those points
which are visited an unusually large number of times.
We prove the analogue of the Erd{\H{o}}s--Taylor
conjecture and obtain the asymptotics for the number of
visits to the most visited site. We also obtain the
asymptotics for the number of points which are visited
very frequently by time $n$. Among the tools we use are
Harnack inequalities and Green's function estimates for
random walks with unbounded jumps; some of these are of
independent interest.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Random walks, Green's functions, Harnack inequalities,
frequent points",
}
@Article{Ivanoff:2007:CCP,
author = "B. Gail Ivanoff and Ely Merzbach and Mathieu Plante",
title = "A Compensator Characterization of Point Processes on
Topological Lattices",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "2:47--2:74",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-390",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/390",
abstract = "We resolve the longstanding question of how to define
the compensator of a point process on a general
partially ordered set in such a way that the
compensator exists, is unique, and characterizes the
law of the process. We define a family of one-parameter
compensators and prove that this family is unique in
some sense and characterizes the finite dimensional
distributions of a totally ordered point process. This
result can then be applied to a general point process
since we prove that such a process can be embedded into
a totally ordered point process on a larger space. We
present some examples, including the partial sum
multiparameter process, single line point processes,
multiparameter renewal processes, and obtain a new
characterization of the two-parameter Poisson process",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "point process, compensator, partial order, single jump
process, partial sum process, adapted random set,
renewal process, Poisson process, multiparameter
martingale",
}
@Article{Luczak:2007:ADC,
author = "Malwina Luczak and Colin McDiarmid",
title = "Asymptotic distributions and chaos for the supermarket
model",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "3:75--3:99",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-391",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/391",
abstract = "In the supermarket model there are $n$ queues, each
with a unit rate server. Customers arrive in a Poisson
process at rate $ \lambda n$, where $ 0 < \lambda < 1$.
Each customer chooses $ d \geq 2$ queues uniformly at
random, and joins a shortest one. It is known that the
equilibrium distribution of a typical queue length
converges to a certain explicit limiting distribution
as $ n \to \infty $. We quantify the rate of
convergence by showing that the total variation
distance between the equilibrium distribution and the
limiting distribution is essentially of order $ 1 / n$
and we give a corresponding result for systems starting
from quite general initial conditions (not in
equilibrium). Further, we quantify the result that the
systems exhibit chaotic behaviour: we show that the
total variation distance between the joint law of a
fixed set of queue lengths and the corresponding
product law is essentially of order at most $ 1 / n$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Supermarket model, join the shortest queue, random
choices, power of two choices, load balancing,
equilibrium, concentration of measure, law of large
numbers, chaos",
}
@Article{Mendez:2007:ETS,
author = "Pedro Mendez",
title = "Exit Times of Symmetric Stable Processes from
Unbounded Convex Domains",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "4:100--4:121",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-393",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/393",
abstract = "We provide several inequalities on the asymptotic
behavior of the harmonic measure of the first exit
position of a $d$-dimensional symmetric stable process
from a unbounded convex domain. Our results on the
harmonic measure will determine the asymptotic behavior
of the distributions of the first exit time from the
domain. These inequalities are given in terms of the
growth of the in radius of the cross sections of the
domain.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "stable process, exit times, unbounded domains",
}
@Article{Heveling:2007:PSC,
author = "Matthias Heveling and Gunter Last",
title = "Point shift characterization of {Palm} measures on
{Abelian} groups",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "5:122--5:137",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-394",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/394",
abstract = "Our first aim in this paper is to characterize Palm
measures of stationary point processes through point
stationarity. This generalizes earlier results from the
Euclidean case to the case of an Abelian group. While a
stationary point process looks statistically the same
from each site, a point stationary point process looks
statistically the same from each of its points. Even in
the Euclidean case our proof will simplify some of the
earlier arguments. A new technical result of some
independent interest is the existence of a complete
countable family of matchings. Using a change of
measure we will generalize our results to discrete
random measures. In the Euclidean case we will finally
treat general random measures by means of a suitable
approximation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "point process, random measure, stationarity,
point-stationarity, Palm measure, matching, bijective
point map",
}
@Article{Uchiyama:2007:AEG,
author = "Kouhei Uchiyama",
title = "Asymptotic Estimates of the {Green} Functions and
Transition Probabilities for {Markov} Additive
Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "6:138--6:180",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-396",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/396",
abstract = "In this paper we shall derive asymptotic expansions of
the Green function and the transition probabilities of
Markov additive (MA) processes $ (\xi_n, S_n) $ whose
first component satisfies Doeblin's condition and the
second one takes valued in $ Z^d $. The derivation is
based on a certain perturbation argument that has been
used in previous works in the same context. In our
asymptotic expansions, however, not only the principal
term but also the second order term are expressed
explicitly in terms of a few basic functions that are
characteristics of the expansion. The second order term
will be important for instance in computation of the
harmonic measures of a half space for certain models.
We introduce a certain aperiodicity condition, named
Condition (AP), that seems a minimal one under which
the Fourier analysis can be applied straightforwardly.
In the case when Condition (AP) is violated the
structure of MA processes will be clarified and it will
be shown that in a simple manner the process, if not
degenerate, are transformed to another one that
satisfies Condition (AP) so that from it we derive
either directly or indirectly (depending on purpose)
the asymptotic expansions for the original process. It
in particular is shown that if the MA processes is
irreducible as a Markov process, then the Green
function is expanded quite similarly to that of a
classical random walk on $ Z^d $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "asymptotic expansion, harmonic analysis, semi-Markov
process, random walk with internal states,
perturbation, aperiodicity, ergodic, Doeblin's
condition",
}
@Article{Pipiras:2007:IRP,
author = "Vladas Pipiras and Murad Taqqu",
title = "Integral representations of periodic and cyclic
fractional stable motions",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "7:181--7:206",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-395",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/395",
abstract = "Stable non-Gaussian self-similar mixed moving averages
can be decomposed into several components. Two of these
are the periodic and cyclic fractional stable motions
which are the subject of this study. We focus on the
structure of their integral representations and show
that the periodic fractional stable motions have, in
fact, a canonical representation. We study several
examples and discuss questions of uniqueness, namely
how to determine whether two given integral
representations of periodic or cyclic fractional stable
motions give rise to the same process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "stable, self-similar processes with stationary
increments, mixed moving averages, periodic and cyclic
flows, cocycles, semi-additive functionals",
}
@Article{Coquet:2007:CVO,
author = "Fran{\c{c}}ois Coquet and Sandrine Toldo",
title = "Convergence of values in optimal stopping and
convergence of optimal stopping times",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "8:207--8:228",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-288",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/288",
abstract = "Under the hypothesis of convergence in probability of
a sequence of c{\`a}dl{\`a}g processes $ (X^n) $ to a
c{\`a}dl{\`a}g process $X$, we are interested in the
convergence of corresponding values in optimal stopping
and also in the convergence of optimal stopping times.
We give results under hypothesis of inclusion of
filtrations or convergence of filtrations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Convergence of filtrations; Convergence of stochastic
processes; Convergence of stopping times.; Optimal
stopping times; Values in optimal stopping",
}
@Article{Labarbe:2007:ABR,
author = "Jean-Maxime Labarbe and Jean-Fran{\c{c}}ois
Marckert",
title = "Asymptotics of {Bernoulli} random walks, bridges,
excursions and meanders with a given number of peaks",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "9:229--9:261",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-397",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/397",
abstract = "A Bernoulli random walk is a random trajectory
starting from 0 and having i.i.d. increments, each of
them being +1 or -1, equally likely. The other families
quoted in the title are Bernoulli random walks under
various conditions. A peak in a trajectory is a local
maximum. In this paper, we condition the families of
trajectories to have a given number of peaks. We show
that, asymptotically, the main effect of setting the
number of peaks is to change the order of magnitude of
the trajectories. The counting process of the peaks,
that encodes the repartition of the peaks in the
trajectories, is also studied. It is shown that
suitably normalized, it converges to a Brownian bridge
which is independent of the limiting trajectory.
Applications in terms of plane trees and parallelogram
polyominoes are provided, as well as an application to
the ``comparison'' between runs and Kolmogorov--Smirnov
statistics.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Bernoulli random walks; bridge; Brownian meander;
excursion; peaks; Weak convergence",
}
@Article{Ganapathy:2007:RM,
author = "Murali Ganapathy",
title = "Robust Mixing",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "10:262--10:299",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-398",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/398",
abstract = "In this paper, we develop a new ``robust mixing''
framework for reasoning about adversarially modified
Markov Chains (AMMC). Let $ \mathbb {P} $ be the
transition matrix of an irreducible Markov Chain with
stationary distribution $ \pi $. An adversary announces
a sequence of stochastic matrices $ \{ \mathbb {A}_t
\}_{t > 0} $ satisfying $ \pi \mathbb {A}_t = \pi $. An
AMMC process involves an application of $ \mathbb {P} $
followed by $ \mathbb {A}_t $ at time $t$. The robust
mixing time of an ergodic Markov Chain $ \mathbb {P}$
is the supremum over all adversarial strategies of the
mixing time of the corresponding AMMC process.
Applications include estimating the mixing times for
certain non-Markovian processes and for reversible
liftings of Markov Chains.\par
{\bf Non-Markovian card shuffling processes}: The
random-to-cyclic transposition process is a {\em
non-Markovian} card shuffling process, which at time
$t$, exchanges the card at position $ L_t := t {\pmod
n}$ with a random card. Mossel, Peres and Sinclair
(2004) showed a lower bound of $ (0.0345 + o(1))n \log
n$ for the mixing time of the random-to-cyclic
transposition process. They also considered a
generalization of this process where the choice of $
L_t$ is adversarial, and proved an upper bound of $ C n
\log n + O(n)$ (with $ C \approx 4 \times 10^5$) on the
mixing time. We reduce the constant to $1$ by showing
that the random-to-top transposition chain ({\em a
Markov Chain}) has robust mixing time $ \leq n \log n +
O(n)$ when the adversarial strategies are limited to
holomorphic strategies, i.e., those strategies which
preserve the symmetry of the underlying Markov Chain.
We also show a $ O(n \log^2 n)$ bound on the robust
mixing time of the lazy random-to-top transposition
chain when the adversary is not limited to holomorphic
strategies.\par
{\bf Reversible liftings}: Chen, Lovasz and Pak showed
that for a reversible ergodic Markov Chain $ \mathbb
{P}$, any reversible lifting $ \mathbb {Q}$ of $
\mathbb {P}$ must satisfy $ \mathcal {T}(\mathbb {P})
\leq \mathcal {T}(\mathbb {Q}) \log (1 / \pi_*)$ where
$ \pi_*$ is the minimum stationary probability. Looking
at a specific adversarial strategy allows us to show
that $ \mathcal {T}(\mathbb {Q}) \geq r(\mathbb {P})$
where $ r(\mathbb {P})$ is the relaxation time of $
\mathbb {P}$. This gives an alternate proof of the
reversible lifting result and helps identify cases
where reversible liftings cannot improve the mixing
time by more than a constant factor.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Markov Chains, Robust mixing time, Reversible lifting,
random-to-cyclic transposition, non-Markovian
processes",
}
@Article{Lachal:2007:FHT,
author = "Aim{\'e} Lachal",
title = "First Hitting Time and Place, Monopoles and Multipoles
for Pseudo-Processes Driven by the Equation {$ \partial
u / \partial t = \pm \partial^N u / \partial x^N $}",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "11:300--11:353",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-399",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/399",
abstract = "Consider the high-order heat-type equation $ \partial
u / \partial t = \pm \partial^N u / \partial x^N $ for
an integer $ N > 2 $ and introduce the related Markov
pseudo-process $ (X(t))_{t \ge 0} $. In this paper, we
study several functionals related to $ (X(t))_{t \ge 0}
$: the maximum $ M(t) $ and minimum $ m(t) $ up to time
$t$; the hitting times $ \tau_a^+$ and $ \tau_a^-$ of
the half lines $ (a, + \infty)$ and $ ( - \infty, a)$
respectively. We provide explicit expressions for the
distributions of the vectors $ (X(t), M(t))$ and $
(X(t), m(t))$, as well as those of the vectors $
(\tau_a^+, X(\tau_a^+))$ and $ (\tau_a^-,
X(\tau_a^-))$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "first hitting time and place; joint distribution of
the process and its maximum/minimum; Multipoles;
pseudo-process; Spitzer's identity",
}
@Article{Valle:2007:EIT,
author = "Glauco Valle",
title = "Evolution of the interfaces in a two dimensional
{Potts} model",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "12:354--12:386",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-346",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/346",
abstract = "We investigate the evolution of the random interfaces
in a two dimensional Potts model at zero temperature
under Glauber dynamics for some particular initial
conditions. We prove that under space-time diffusive
scaling the shape of the interfaces converges in
probability to the solution of a non-linear parabolic
equation. This Law of Large Numbers is obtained from
the Hydrodynamic limit of a coupling between an
exclusion process and an inhomogeneous one dimensional
zero range process with asymmetry at the origin.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Exclusion Processes, Interface Dynamics, Hydrodynamic
limit",
}
@Article{Masiero:2007:RPT,
author = "Federica Masiero",
title = "Regularizing Properties for Transition Semigroups and
Semilinear Parabolic Equations in {Banach} Spaces",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "13:387--13:419",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-401",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/401",
abstract = "We study regularizing properties for transition
semigroups related to Ornstein Uhlenbeck processes with
values in a Banach space $E$ which is continuously and
densely embedded in a real and separable Hilbert space
$H$. Namely we study conditions under which the
transition semigroup maps continuous and bounded
functions into differentiable functions. Via a Girsanov
type theorem such properties extend to perturbed
Ornstein Uhlenbeck processes. We apply the results to
solve in mild sense semilinear versions of Kolmogorov
equations in $E$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Banach spaces.; Ornstein--Uhlenbeck and perturbed
Ornstein--Uhlenbeck transition semigroups; parabolic
equations; regularizing properties",
}
@Article{Lambert:2007:QSD,
author = "Amaury Lambert",
title = "Quasi-Stationary Distributions and the
Continuous-State Branching Process Conditioned to Be
Never Extinct",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "14:420--14:446",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-402",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/402",
abstract = "We consider continuous-state branching (CB) processes
which become extinct (i.e., hit 0) with positive
probability. We characterize all the quasi-stationary
distributions (QSD) for the CB-process as a
stochastically monotone family indexed by a real
number. We prove that the minimal element of this
family is the so-called Yaglom quasi-stationary
distribution, that is, the limit of one-dimensional
marginals conditioned on being nonzero. Next, we
consider the branching process conditioned on not being
extinct in the distant future, or $Q$-process, defined
by means of Doob $h$-transforms. We show that the
$Q$-process is distributed as the initial CB-process
with independent immigration, and that under the $ L
\log L$ condition, it has a limiting law which is the
size-biased Yaglom distribution (of the CB-process).
More generally, we prove that for a wide class of
nonnegative Markov processes absorbed at 0 with
probability 1, the Yaglom distribution is always
stochastically dominated by the stationary probability
of the $Q$-process, assuming that both exist. Finally,
in the diffusion case and in the stable case, the
$Q$-process solves a SDE with a drift term that can be
seen as the instantaneous immigration.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Continuous-state branching process; h-transform;
immigration; L{\'e}vy process; Q-process;
quasi-stationary distribution; size-biased
distribution; stochastic differential equations; Yaglom
theorem",
}
@Article{Giovanni:2007:SCG,
author = "Peccati Giovanni and Murad Taqqu",
title = "Stable convergence of generalized {$ L^2 $} stochastic
integrals and the principle of conditioning",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "15:447--15:480",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-404",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/404",
abstract = "We consider generalized adapted stochastic integrals
with respect to independently scattered random measures
with second moments, and use a decoupling technique,
formulated as a \flqq principle of conditioning\frqq,
to study their stable convergence towards mixtures of
infinitely divisible distributions. The goal of this
paper is to develop the theory. Our results apply, in
particular, to Skorohod integrals on abstract Wiener
spaces, and to multiple integrals with respect to
independently scattered and finite variance random
measures. The first application is discussed in some
detail in the final section of the present work, and
further extended in a companion paper (Peccati and
Taqqu (2006b)). Applications to the stable convergence
(in particular, central limit theorems) of multiple
Wiener--It{\^o} integrals with respect to independently
scattered (and not necessarily Gaussian) random
measures are developed in Peccati and Taqqu (2006a,
2007). The present work concludes with an example
involving quadratic Brownian functionals.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Decoupling; Generalized stochastic integrals;
Independently scattered measures; multiple Poisson
integrals; Principle of conditioning; Resolutions of
the identity; Skorohod integrals; Stable convergence;
Weak convergence",
}
@Article{Galvin:2007:SCR,
author = "David Galvin",
title = "Sampling $3$-colourings of regular bipartite graphs",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "16:481--16:497",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-403",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/403",
abstract = "We show that if $ G = (V, E) $ is a regular bipartite
graph for which the expansion of subsets of a single
parity of $V$ is reasonably good and which satisfies a
certain local condition (that the union of the
neighbourhoods of adjacent vertices does not contain
too many pairwise non-adjacent vertices), and if $M$ is
a Markov chain on the set of proper 3-colourings of $G$
which updates the colour of at most $ c|V|$ vertices at
each step and whose stationary distribution is uniform,
then for $ c < .22$ and $d$ sufficiently large the
convergence to stationarity of $M$ is (essentially)
exponential in $ |V|$. In particular, if $G$ is the
$d$-dimensional hypercube $ Q_d$ (the graph on vertex
set $ \{ 0, 1 \}^d$ in which two strings are adjacent
if they differ on exactly one coordinate) then the
convergence to stationarity of the well-known Glauber
(single-site update) dynamics is exponentially slow in
$ 2^d / (\sqrt {d} \log d)$. A combinatorial corollary
of our main result is that in a uniform 3-colouring of
$ Q_d$ there is an exponentially small probability (in
$ 2^d$) that there is a colour $i$ such the proportion
of vertices of the even subcube coloured $i$ differs
from the proportion of the odd subcube coloured $i$ by
at most $ .22$. Our proof combines a conductance
argument with combinatorial enumeration methods.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Mixing time, 3-colouring, Potts model, conductance,
Glauber dynamics, discrete hypercube",
}
@Article{Evans:2007:ECE,
author = "Steven Evans and Tye Lidman",
title = "Expectation, Conditional Expectation and Martingales
in Local Fields",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "17:498--17:515",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-405",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/405",
abstract = "We investigate a possible definition of expectation
and conditional expectation for random variables with
values in a local field such as the $p$-adic numbers.
We define the expectation by analogy with the
observation that for real-valued random variables in $
L^2$ the expected value is the orthogonal projection
onto the constants. Previous work has shown that the
local field version of $ L^\infty $ is the appropriate
counterpart of $ L^2$, and so the expected value of a
local field-valued random variable is defined to be its
``projection'' in $ L^\infty $ onto the
constants.\par
Unlike the real case, the resulting projection is not
typically a single constant, but rather a ball in the
metric on the local field. However, many properties of
this expectation operation and the corresponding
conditional expectation mirror those familiar from the
real-valued case; for example, conditional expectation
is, in a suitable sense, a contraction on $ L^\infty $
and the tower property holds. We also define the
corresponding notion of martingale, show that several
standard examples of martingales (for example, sums or
products of suitable independent random variables or
``harmonic'' functions composed with Markov chains)
have local field analogues, and obtain versions of the
optional sampling and martingale convergence
theorems.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "conditional expectation; expectation; local field;
martingale; martingale convergence; optional sampling;
projection",
}
@Article{Gartner:2007:ICS,
author = "J{\"u}rgen G{\"a}rtner and Frank den Hollander and
Gregory Maillard",
title = "Intermittency on catalysts: symmetric exclusion",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "18:516--18:573",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-407",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/407",
abstract = "We continue our study of intermittency for the
parabolic Anderson equation, i.e., the spatially
discrete heat equation on the d-dimensional integer
lattice with a space-time random potential. The
solution of the equation describes the evolution of a
``reactant'' under the influence of a ``catalyst''.
In this paper we focus on the case where the random
field is an exclusion process with a symmetric random
walk transition kernel, starting from Bernoulli
equilibrium. We consider the annealed Lyapunov
exponents, i.e., the exponential growth rates of the
successive moments of the solution. We show that these
exponents are trivial when the random walk is
recurrent, but display an interesting dependence on the
diffusion constant when the random walk is transient,
with qualitatively different behavior in different
dimensions. Special attention is given to the
asymptotics of the exponents when the diffusion
constant tends to infinity, which is controlled by
moderate deviations of the random field requiring a
delicate expansion argument.\par
In G{\"a}rtner and den Hollander [10] the case of a
Poisson field of independent (simple) random walks was
studied. The two cases show interesting differences and
similarities. Throughout the paper, a comparison of the
two cases plays a crucial role.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "catalytic random medium; exclusion processes;
intermittency; Lyapunov exponents; Parabolic Anderson
model",
}
@Article{Warren:2007:DBM,
author = "Jon Warren",
title = "{Dyson}'s {Brownian} motions, intertwining and
interlacing",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "19:573--19:590",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-406",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/406",
abstract = "A reflected Brownian motion in the Gelfand--Tsetlin
cone is used to construct Dyson's process of
non-colliding Brownian motions. The key step of the
construction is to consider two interlaced families of
Brownian paths with paths belonging to the second
family reflected off paths belonging to the first. Such
families of paths are known to arise in the Arratia
flow of coalescing Brownian motions. A determinantal
formula for the distribution of coalescing Brownian
motions is presented.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "coalescing Brownian motions; Gelfand--Tsetlin cone.;
intertwining; non-colliding Brownian motions",
}
@Article{Benjamini:2007:RSR,
author = "Itai Benjamini and Roey Izkovsky and Harry Kesten",
title = "On the Range of the Simple Random Walk Bridge on
Groups",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "20:591--20:612",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-408",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/408",
abstract = "Let $G$ be a vertex transitive graph. A study of the
range of simple random walk on $G$ and of its bridge is
proposed. While it is expected that on a graph of
polynomial growth the sizes of the range of the
unrestricted random walk and of its bridge are the same
in first order, this is not the case on some larger
graphs such as regular trees. Of particular interest is
the case when $G$ is the Cayley graph of a group. In
this case we even study the range of a general
symmetric (not necessarily simple) random walk on $G$.
We hope that the few examples for which we calculate
the first order behavior of the range here will help to
discover some relation between the group structure and
the behavior of the range. Further problems regarding
bridges are presented.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "range of a bridge; range of random walk",
}
@Article{Toninelli:2007:CLR,
author = "Fabio Lucio Toninelli",
title = "Correlation Lengths for Random Polymer Models and for
Some Renewal Sequences",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "21:613--21:636",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-414",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/414",
abstract = "We consider models of directed polymers interacting
with a one-dimensional defect line on which random
charges are placed. More abstractly, one starts from
renewal sequence on $Z$ and gives a random
(site-dependent) reward or penalty to the occurrence of
a renewal at any given point of $Z$. These models are
known to undergo a delocalization-localization
transition, and the free energy $F$ vanishes when the
critical point is approached from the localized region.
We prove that the quenched correlation length $ \xi $,
defined as the inverse of the rate of exponential decay
of the two-point function, does not diverge faster than
$ 1 / F$. We prove also an exponentially decaying upper
bound for the disorder-averaged two-point function,
with a good control of the sub-exponential prefactor.
We discuss how, in the particular case where disorder
is absent, this result can be seen as a refinement of
the classical renewal theorem, for a specific class of
renewal sequences.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Pinning and Wetting Models, Typical and Average
Correlation Lengths, Critical Exponents, Renewal
Theory, Exponential Convergence Rates",
}
@Article{Matzinger:2007:DLP,
author = "Heinrich Matzinger and Serguei Popov",
title = "Detecting a Local Perturbation in a Continuous
Scenery",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "22:637--22:660",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-409",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/409",
abstract = "A continuous one-dimensional scenery is a
double-infinite sequence of points (thought of as
locations of {\em bells}) in $R$. Assume that a scenery
$X$ is observed along the path of a Brownian motion in
the following way: when the Brownian motion encounters
a bell different from the last one visited, we hear a
ring. The trajectory of the Brownian motion is unknown,
whilst the scenery $X$ is known except in some finite
interval. We prove that given only the sequence of
times of rings, we can a.s. reconstruct the scenery $X$
entirely. For this we take the scenery$X$ to be a local
perturbation of a Poisson scenery $ X'$. We present an
explicit reconstruction algorithm. This problem is the
continuous analog of the ``detection of a defect in a
discrete scenery''. Many of the essential techniques
used with discrete sceneries do not work with
continuous sceneries.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion, Poisson process, localization test,
detecting defects in sceneries seen along random
walks",
}
@Article{Dietz:2007:OLS,
author = "Zach Dietz and Sunder Sethuraman",
title = "Occupation laws for some time-nonhomogeneous {Markov}
chains",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "23:661--23:683",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-413",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/413",
abstract = "We consider finite-state time-nonhomogeneous Markov
chains whose transition matrix at time $n$ is $ I + G /
n^z$ where $G$ is a ``generator'' matrix, that is $
G(i, j) > 0$ for $ i, j$ distinct, and $ G(i, i) = -
\sum_{k \ne i} G(i, k)$, and $ z > 0$ is a strength
parameter. In these chains, as time grows, the
positions are less and less likely to change, and so
form simple models of age-dependent time-reinforcing
schemes. These chains, however, exhibit a trichotomy of
occupation behaviors depending on parameters.\par
We show that the average occupation or empirical
distribution vector up to time $n$, when variously $ 0
< z < 1$, $ z > 1$ or $ z = 1$, converges in
probability to a unique ``stationary'' vector $ n_G$,
converges in law to a nontrivial mixture of point
measures, or converges in law to a distribution $ m_G$
with no atoms and full support on a simplex
respectively, as $n$ tends to infinity. This last type
of limit can be interpreted as a sort of ``spreading''
between the cases $ 0 < z < 1$ and $ z > 1$.\par
In particular, when $G$ is appropriately chosen, $ m_G$
is a Dirichlet distribution, reminiscent of results in
Polya urns.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "laws of large numbers, nonhomogeneous, Markov,
occupation, reinforcement, Dirichlet distribution",
}
@Article{Ferrari:2007:QSD,
author = "Pablo Ferrari and Nevena Maric",
title = "Quasi Stationary Distributions and {Fleming--Viot}
Processes in Countable Spaces",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "24:684--24:702",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-415",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/415",
abstract = "We consider an irreducible pure jump Markov process
with rates $ Q = (q(x, y)) $ on $ \Lambda \cup \{ 0 \}
$ with $ \Lambda $ countable and $0$ an absorbing
state. A {\em quasi stationary distribution \rm} (QSD)
is a probability measure $ \nu $ on $ \Lambda $ that
satisfies: starting with $ \nu $, the conditional
distribution at time $t$, given that at time $t$ the
process has not been absorbed, is still $ \nu $. That
is, $ \nu (x) = \nu P_t(x) / (\sum_{y \in \Lambda } \nu
P_t(y))$, with $ P_t$ the transition probabilities for
the process with rates $Q$.\par
A {\em Fleming--Viot} (FV) process is a system of $N$
particles moving in $ \Lambda $. Each particle moves
independently with rates $Q$ until it hits the
absorbing state $0$; but then instantaneously chooses
one of the $ N - 1$ particles remaining in $ \Lambda $
and jumps to its position. Between absorptions each
particle moves with rates $Q$ independently.\par
Under the condition $ \alpha := \sum_{x \in \Lambda }
\inf Q(\cdot, x) > \sup Q(\cdot, 0) := C$ we prove
existence of QSD for $Q$; uniqueness has been proven by
Jacka and Roberts. When $ \alpha > 0$ the FV process is
ergodic for each $N$. Under $ \alpha > C$ the mean
normalized densities of the FV unique stationary
measure converge to the QSD of $Q$, as $ N \to \infty
$; in this limit the variances vanish.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Fleming--Viot process; Quasi stationary
distributions",
}
@Article{vanderHofstad:2007:DRG,
author = "Remco van der Hofstad and Gerard Hooghiemstra and
Dmitri Znamenski",
title = "Distances in Random Graphs with Finite Mean and
Infinite Variance Degrees",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "25:703--25:766",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-420",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/420",
abstract = "In this paper we study typical distances in random
graphs with i.i.d. degrees of which the tail of the
common distribution function is regularly varying with
exponent $ 1 - \tau $. Depending on the value of the
parameter $ \tau $ we can distinct three cases: (i) $
\tau > 3 $, where the degrees have finite variance,
(ii) $ \tau \in (2, 3) $, where the degrees have
infinite variance, but finite mean, and (iii) $ \tau
\in (1, 2) $, where the degrees have infinite mean. The
distances between two randomly chosen nodes belonging
to the same connected component, for $ \tau > 3 $ and $
\tau \in (1, 2), $ have been studied in previous
publications, and we survey these results here. When $
\tau \in (2, 3) $, the graph distance centers around $
2 \log \log {N} / | \log (\tau - 2)| $. We present a
full proof of this result, and study the fluctuations
around this asymptotic means, by describing the
asymptotic distribution. The results presented here
improve upon results of Reittu and Norros, who prove an
upper bound only.\par
The random graphs studied here can serve as models for
complex networks where degree power laws are observed;
this is illustrated by comparing the typical distance
in this model to Internet data, where a degree power
law with exponent $ \tau \approx 2.2 $ is observed for
the so-called Autonomous Systems (AS) graph",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Branching processes, configuration model, coupling,
graph distance",
}
@Article{Gnedin:2007:CR,
author = "Alexander Gnedin",
title = "The Chain Records",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "26:767--26:786",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-410",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/410",
abstract = "Chain records is a new type of multidimensional
record. We discuss how often the chain records occur
when the background sampling is from the unit cube with
uniform distribution (or, more generally, from an
arbitrary continuous product distribution in d
dimensions). Extensions are given for sampling from
more general spaces with a self-similarity property.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "chains; Ewens partition; multidimensional records;
random orders",
}
@Article{Feng:2007:LDD,
author = "Shui Feng",
title = "Large Deviations for {Dirichlet} Processes and
{Poisson--Dirichlet} Distribution with Two Parameters",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "27:787--27:807",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-417",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/417",
abstract = "Large deviation principles are established for the
two-parameter Poisson--Dirichlet distribution and
two-parameter Dirichlet process when parameter $ \theta
$ approaches infinity. The motivation for these results
is to understand the differences in terms of large
deviations between the two-parameter models and their
one-parameter counterparts. New insight is obtained
about the role of the second parameter $ \alpha $
through a comparison with the corresponding results for
the one-parameter Poisson--Dirichlet distribution and
Dirichlet process.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Dirichlet processes; GEM representation; large
deviations; Poisson--Dirichlet distribution",
}
@Article{Taylor:2007:CAP,
author = "Jesse Taylor",
title = "The Common Ancestor Process for a {Wright--Fisher}
Diffusion",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "28:808--28:847",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-418",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/418",
abstract = "Rates of molecular evolution along phylogenetic trees
are influenced by mutation, selection and genetic
drift. Provided that the branches of the tree
correspond to lineages belonging to genetically
isolated populations (e.g., multi-species phylogenies),
the interplay between these three processes can be
described by analyzing the process of substitutions to
the common ancestor of each population. We characterize
this process for a class of diffusion models from
population genetics theory using the structured
coalescent process introduced by Kaplan et al. (1988)
and formalized in Barton et al. (2004). For two-allele
models, this approach allows both the stationary
distribution of the type of the common ancestor and the
generator of the common ancestor process to be
determined by solving a one-dimensional boundary value
problem. In the case of a Wright--Fisher diffusion with
genic selection, this solution can be found in closed
form, and we show that our results complement those
obtained by Fearnhead (2002) using the ancestral
selection graph. We also observe that approximations
which neglect recurrent mutation can significantly
underestimate the exact substitution rates when
selection is strong. Furthermore, although we are
unable to find closed-form expressions for models with
frequency-dependent selection, we can still solve the
corresponding boundary value problem numerically and
then use this solution to calculate the substitution
rates to the common ancestor. We illustrate this
approach by studying the effect of dominance on the
common ancestor process in a diploid population.
Finally, we show that the theory can be formally
extended to diffusion models with more than two genetic
backgrounds, but that it leads to systems of singular
partial differential equations which we have been
unable to solve.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Common-ancestor process; diffusion process; genetic
drift; selection; structured coalescent; substitution
rates",
}
@Article{Gautier:2007:SNS,
author = "Eric Gautier",
title = "Stochastic Nonlinear {Schr{\"o}dinger} Equations
Driven by a Fractional Noise. {Well}-Posedness, Large
Deviations and Support",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "29:848--29:861",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-416",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/416",
abstract = "We consider stochastic nonlinear Schrodinger equations
driven by an additive noise. The noise is fractional in
time with Hurst parameter $ H \in (0, 1) $ and colored
in space with a nuclear space correlation operator. We
study local well-posedness. Under adequate assumptions
on the initial data, the space correlations of the
noise and for some saturated nonlinearities, we prove
sample path large deviations and support results in a
space of Holder continuous in time until blow-up paths.
We consider Kerr nonlinearities when $ H > 1 / 2 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "fractional Brownian motion; Large deviations;
nonlinear Schrodinger equation; stochastic partial
differential equations",
}
@Article{Hambly:2007:NVP,
author = "Ben Hambly and Liza Jones",
title = "Number variance from a probabilistic perspective:
infinite systems of independent {Brownian} motions and
symmetric alpha stable processes",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "30:862--30:887",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-419",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
note = "See erratum \cite{Hambly:2009:ENV}.",
URL = "http://ejp.ejpecp.org/article/view/419",
abstract = "Some probabilistic aspects of the number variance
statistic are investigated. Infinite systems of
independent Brownian motions and symmetric alpha-stable
processes are used to construct explicit new examples
of processes which exhibit both divergent and
saturating number variance behaviour. We derive a
general expression for the number variance for the
spatial particle configurations arising from these
systems and this enables us to deduce various limiting
distribution results for the fluctuations of the
associated counting functions. In particular, knowledge
of the number variance allows us to introduce and
characterize a novel family of centered, long memory
Gaussian processes. We obtain fractional Brownian
motion as a weak limit of these constructed
processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "controlled variability; fractional Brownian motion;
functional limits; Gaussian fluctuations; Gaussian
processes; long memory; Number variance; symmetric
alpha-stable processes",
}
@Article{Weill:2007:ARB,
author = "Mathilde Weill",
title = "Asymptotics for Rooted Bipartite Planar Maps and
Scaling Limits of Two-Type Spatial Trees",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "31:862--31:925",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-425",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/425",
abstract = "We prove some asymptotic results for the radius and
the profile of large random bipartite planar maps.
Using a bijection due to Bouttier, Di Francesco and
Guitter between rooted bipartite planar maps and
certain two-type trees with positive labels, we derive
our results from a conditional limit theorem for
two-type spatial trees. Finally we apply our estimates
to separating vertices of bipartite planar maps: with
probability close to one when n tends to infinity, a
random $ 2 k$-angulation with n faces has a separating
vertex whose removal disconnects the map into two
components each with size greater that $ n^{1 / 2 -
\varepsilon }$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Conditioned Brownian snake; Planar maps; two-type
Galton--Watson trees",
}
@Article{Benjamini:2007:RGH,
author = "Itai Benjamini and Ariel Yadin and Amir Yehudayoff",
title = "Random Graph-Homomorphisms and Logarithmic Degree",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "32:926--32:950",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-427",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/427",
abstract = "A graph homomorphism between two graphs is a map from
the vertex set of one graph to the vertex set of the
other graph, that maps edges to edges. In this note we
study the range of a uniformly chosen homomorphism from
a graph $G$ to the infinite line $Z$. It is shown that
if the maximal degree of $G$ is `sub-logarithmic', then
the range of such a homomorphism is
super-constant.\par
Furthermore, some examples are provided, suggesting
that perhaps for graphs with super-logarithmic degree,
the range of a typical homomorphism is bounded. In
particular, a sharp transition is shown for a specific
family of graphs $ C_{n, k}$ (which is the tensor
product of the $n$-cycle and a complete graph, with
self-loops, of size $k$). That is, given any function $
\psi (n)$ tending to infinity, the range of a typical
homomorphism of $ C_{n, k}$ is super-constant for $ k =
2 \log (n) - \psi (n)$, and is $3$ for $ k = 2 \log (n)
+ \psi (n)$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Kurtz:2007:YWE,
author = "Thomas Kurtz",
title = "The {Yamada--Watanabe--Engelbert} theorem for general
stochastic equations and inequalities",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "33:951--33:965",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-431",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/431",
abstract = "A general version of the Yamada--Watanabe and
Engelbert results relating existence and uniqueness of
strong and weak solutions for stochastic equations is
given. The results apply to a wide variety of
stochastic equations including classical stochastic
differential equations, stochastic partial differential
equations, and equations involving multiple time
transformations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "weak solution, strong solution, pathwise uniqueness,
stochastic differential equations, stochastic partial
differential equations, multidimensional index",
}
@Article{Major:2007:MVB,
author = "Peter Major",
title = "On a Multivariate Version of {Bernstein}'s
Inequality",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "34:966--34:988",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-430",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/430",
abstract = "We prove such a multivariate version of Bernstein's
inequality about the tail distribution of degenerate
$U$-statistics which is an improvement of some former
results. This estimate will be compared with an
analogous bound about the tail distribution of multiple
Wiener--It{\^o} integrals. Their comparison shows that
our estimate is sharp. The proof is based on good
estimates about high moments of degenerate
$U$-statistics. They are obtained by means of a diagram
formula which enables us to express the product of
degenerate $U$-statistics as the sum of such
expressions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Bernstein inequality, (degenerate) U-statistics,
Wiener--It{\^o} integrals, diagram formula, moment
estimates",
}
@Article{Penrose:2007:GLR,
author = "Mathew Penrose",
title = "{Gaussian} Limts for Random Geometric Measures",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "35:989--35:1035",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-429",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/429",
abstract = "Given $n$ independent random marked $d$-vectors $ X_i$
with a common density, define the measure $ \nu_n =
\sum_i \xi_i $, where $ \xi_i$ is a measure (not
necessarily a point measure) determined by the
(suitably rescaled) set of points near $ X_i$.
Technically, this means here that $ \xi_i$ stabilizes
with a suitable power-law decay of the tail of the
radius of stabilization. For bounded test functions $f$
on $ R^d$, we give a central limit theorem for $
\nu_n(f)$, and deduce weak convergence of $
\nu_n(\cdot)$, suitably scaled and centred, to a
Gaussian field acting on bounded test functions. The
general result is illustrated with applications to
measures associated with germ-grain models, random and
cooperative sequential adsorption, Voronoi tessellation
and $k$-nearest neighbours graph.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Random measures",
}
@Article{Turova:2007:CPT,
author = "Tatyana Turova",
title = "Continuity of the percolation threshold in randomly
grown graphs",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "36:1036--36:1047",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-436",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/436",
abstract = "We consider various models of randomly grown graphs.
In these models the vertices and the edges accumulate
within time according to certain rules. We study a
phase transition in these models along a parameter
which refers to the mean life-time of an edge. Although
deleting old edges in the uniformly grown graph changes
abruptly the properties of the model, we show that some
of the macro-characteristics of the graph vary
continuously. In particular, our results yield a lower
bound for the size of the largest connected component
of the uniformly grown graph.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "branching processes; Dynamic random graphs; phase
transition",
}
@Article{Johansson:2007:EEG,
author = "Kurt Johansson and Eric Nordenstam",
title = "Erratum to {``Eigenvalues of GUE Minors''}",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "37:1048--37:1051",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-816",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
note = "See \cite{Johansson:2006:EGM}.",
URL = "http://ejp.ejpecp.org/article/view/816",
abstract = "In the paper
\url{http://www.math.washington.edu/~ejpecp/viewarticle.php?id=1647},
two expressions for the so called GUE minor kernel are
presented, one in definition 1.2 and one in the
formulas (5.6) and (5.7). The expressions given in
(5.6) and (5.7) are correct, but the expression in
definition 1.2 of the paper has to be modified in the
case $ r > s $. The proof of the equality of the two
expressions for the GUE minor kernel given in the paper
was based on lemma 5.6 which is not correct since some
terms in the expansion are missing. The correct
expansion is given in lemma 1.2 below.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Arias-Castro:2007:IRH,
author = "Ery Arias-Castro",
title = "Interpolation of Random Hyperplanes",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "38:1052--38:1071",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-435",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/435",
abstract = "Let $ \{ (Z_i, W_i) \colon i = 1, \dots, n \} $ be
uniformly distributed in $ [0, 1]^d \times \mathbb
{G}(k, d) $, where $ \mathbb {G}(k, d) $ denotes the
space of $k$-dimensional linear subspaces of $ \mathbb
{R}^d$. For a differentiable function $ f \colon [0,
1]^k \rightarrow [0, 1]^d$, we say that $f$
interpolates $ (z, w) \in [0, 1]^d \times \mathbb
{G}(k, d)$ if there exists $ x \in [0, 1]^k$ such that
$ f(x) = z$ and $ \vec {f}(x) = w$, where $ \vec
{f}(x)$ denotes the tangent space at $x$ defined by
$f$. For a smoothness class $ {\cal F}$ of Holder type,
we obtain probability bounds on the maximum number of
points a function $ f \in {\cal F}$ interpolates.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Grassmann Manifold; Haar Measure; Kolmogorov Entropy;
Pattern Recognition",
}
@Article{Bobkov:2007:LDI,
author = "Sergey Bobkov",
title = "Large deviations and isoperimetry over convex
probability measures with heavy tails",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "39:1072--39:1100",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-440",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/440",
abstract = "Large deviations and isoperimetric inequalities are
considered for probability distributions, satisfying
convexity conditions of the Brunn--Minkowski-type",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Large deviations, convex measures, dilation of sets,
transportation of mass, Khinchin-type, isoperimetric,
weak Poincar{\'e}, Sobolev-type inequalities",
}
@Article{Griffiths:2007:RIA,
author = "Robert Griffiths and Dario Spano",
title = "Record Indices and Age-Ordered Frequencies in
Exchangeable {Gibbs} Partitions",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "40:1101--40:1130",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-434",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/434",
abstract = "The frequencies of an exchangeable Gibbs random
partition of the integers (Gnedin and Pitman 2005) are
considered in their age-order, i.e., their size-biased
order. We study their dependence on the sequence of
record indices (i.e., the least elements) of the blocks
of the partition. In particular we show that,
conditionally on the record indices, the distribution
of the age-ordered frequencies has a left-neutral
stick-breaking structure. Such a property in fact
characterizes the Gibbs family among all exchangeable
partitions and leads to further interesting results on:
(i) the conditional Mellin transform of the $k$-th
oldest frequency given the $k$-th record index, and
(ii) the conditional distribution of the first $k$
normalized frequencies, given their sum and the $k$-th
record index; the latter turns out to be a mixture of
Dirichlet distributions. Many of the mentioned
representations are extensions of Griffiths and Lessard
(2005) results on Ewens' partitions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Exchangeable Gibbs Partitions, GEM distribution,
Age-ordered frequencies, Beta-Stacy distribution,
Neutral distributions, Record indices",
}
@Article{Maida:2007:LDL,
author = "Myl{\`e}ne Maida",
title = "Large deviations for the largest eigenvalue of rank
one deformations of {Gaussian} ensembles",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "41:1131--41:1150",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-438",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/438",
abstract = "We establish a large deviation principle for the
largest eigenvalue of a rank one deformation of a
matrix from the GUE or GOE. As a corollary, we get
another proof of the phenomenon, well-known in learning
theory and finance, that the largest eigenvalue
separates from the bulk when the perturbation is large
enough. A large part of the paper is devoted to an
auxiliary result on the continuity of spherical
integrals in the case when one of the matrix is of rank
one, as studied in one of our previous works.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "large deviations; random matrices",
}
@Article{Evans:2007:AEA,
author = "Steven Evans and Tye Lidman",
title = "Asymptotic Evolution of Acyclic Random Mappings",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "42:1051--42:1180",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-437",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/437",
abstract = "An acyclic mapping from an $n$ element set into itself
is a mapping $ \varphi $ such that if $ \varphi^k(x) =
x$ for some $k$ and $x$, then $ \varphi (x) = x$.
Equivalently, $ \varphi^\ell = \varphi^{\ell + 1} =
\ldots $ for $ \ell $ sufficiently large. We
investigate the behavior as $ n \rightarrow \infty $ of
a sequence of a Markov chain on the collection of such
mappings. At each step of the chain, a point in the $n$
element set is chosen uniformly at random and the
current mapping is modified by replacing the current
image of that point by a new one chosen independently
and uniformly at random, conditional on the resulting
mapping being again acyclic. We can represent an
acyclic mapping as a directed graph (such a graph will
be a collection of rooted trees) and think of these
directed graphs as metric spaces with some extra
structure. Informal calculations indicate that the
metric space valued process associated with the Markov
chain should, after an appropriate time and ``space''
rescaling, converge as $ n \rightarrow \infty $ to a
real tree ($R$-tree) valued Markov process that is
reversible with respect to a measure induced naturally
by the standard reflected Brownian bridge. Although we
don't prove such a limit theorem, we use Dirichlet form
methods to construct a Markov process that is Hunt with
respect to a suitable Gromov--Hausdorff-like metric and
evolves according to the dynamics suggested by the
heuristic arguments. This process is similar to one
that appears in earlier work by Evans and Winter as a
similarly informal limit of a Markov chain related to
the subtree prune and regraft tree (SPR) rearrangements
from phylogenetics.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian bridge; Brownian excursion; continuum random
tree; Dirichlet form; excursion theory;
Gromov--Hausdorff metric; path decomposition; random
mapping",
}
@Article{Darses:2007:TRD,
author = "Sebastien Darses and Bruno Saussereau",
title = "Time Reversal for Drifted Fractional {Brownian} Motion
with {Hurst} Index {$ H > 1 / 2 $}",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "43:1181--43:1211",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-439",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/439",
abstract = "Let $X$ be a drifted fractional Brownian motion with
Hurst index $ H > 1 / 2$. We prove that there exists a
fractional backward representation of $X$, i.e., the
time reversed process is a drifted fractional Brownian
motion, which continuously extends the one obtained in
the theory of time reversal of Brownian diffusions when
$ H = 1 / 2$. We then apply our result to stochastic
differential equations driven by a fractional Brownian
motion.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Fractional Brownian motion; Malliavin Calculus.; Time
reversal",
}
@Article{Barthe:2007:IBE,
author = "Franck Barthe and Patrick Cattiaux and Cyril
Roberto",
title = "Isoperimetry between exponential and {Gaussian}",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "44:1212--44:1237",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-441",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/441",
abstract = "We study the isoperimetric problem for product
probability measures with tails between the exponential
and the Gaussian regime. In particular we exhibit many
examples where coordinate half-spaces are approximate
solutions of the isoperimetric problem",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Isoperimetry; Super-Poincar{\'e} inequality",
}
@Article{Rider:2007:CDP,
author = "Brian Rider and Balint Virag",
title = "Complex Determinantal Processes and {$ H1 $} Noise",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "45:1238--45:1257",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-446",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/446",
abstract = "For the plane, sphere, and hyperbolic plane we
consider the canonical invariant determinantal point
processes $ \mathcal Z_\rho $ with intensity $ \rho d
\nu $, where $ \nu $ is the corresponding invariant
measure. We show that as $ \rho \to \infty $, after
centering, these processes converge to invariant $ H^1
$ noise. More precisely, for all functions $ f \in H^1
(\nu) \cap L^1 (\nu) $ the distribution of $ \sum_{z
\in \mathcal Z} f(z) - \frac {\rho }{\pi } \int f d \nu
$ converges to Gaussian with mean zero and variance $
\frac {1}{4 \pi } \| f \|_{H^1}^2 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "determinantal process; invariant point process; noise
limit; random matrices",
}
@Article{Neunhauserer:2007:RWI,
author = "J{\"o}rg Neunh{\"a}userer",
title = "Random walks on infinite self-similar graphs",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "46:1258--46:1275",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-448",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/448",
abstract = "We introduce a class of rooted infinite self-similar
graphs containing the well known Fibonacci graph and
graphs associated with Pisot numbers. We consider
directed random walks on these graphs and study their
entropy and their limit measures. We prove that every
infinite self-similar graph has a random walk of full
entropy and that the limit measures of this random
walks are absolutely continuous.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "graph; random walk",
}
@Article{Klass:2007:UAQ,
author = "Michael Klass and Krzysztof Nowicki",
title = "Uniformly Accurate Quantile Bounds Via The Truncated
Moment Generating Function: The Symmetric Case",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "47:1276--47:1298",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-452",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/452",
abstract = "Let $ X_1, X_2, \dots $ be independent and symmetric
random variables such that $ S_n = X_1 + \cdots + X_n $
converges to a finite valued random variable $S$ a.s.
and let $ S^* = \sup_{1 \leq n \leq \infty } S_n$
(which is finite a.s.). We construct upper and lower
bounds for $ s_y$ and $ s_y^*$, the upper $ 1 / y$-th
quantile of $ S_y$ and $ S^*$, respectively. Our
approximations rely on an explicitly computable
quantity $ \underline q_y$ for which we prove that\par
$$ \frac 1 2 \underline q_{y / 2} < s_y^* < 2
\underline q_{2y} \quad \text { and } \quad \frac 1 2
\underline q_{ (y / 4) (1 + \sqrt { 1 - 8 / y})} < s_y
< 2 \underline q_{2y}. $$
The RHS's hold for $ y \geq 2$ and the LHS's for $ y
\geq 94$ and $ y \geq 97$, respectively. Although our
results are derived primarily for symmetric random
variables, they apply to non-negative variates and
extend to an absolute value of a sum of independent but
otherwise arbitrary random variables.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Sum of independent rv's, tail distributions, tail
distributions, tail probabilities, quantile
approximation, Hoffmann--J{\o}rgensen/Klass--Nowicki
Inequality",
}
@Article{Grigorescu:2007:EPM,
author = "Ilie Grigorescu and Min Kang",
title = "Ergodic Properties of Multidimensional {Brownian}
Motion with Rebirth",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "48:1299--48:1322",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-450",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/450",
abstract = "In a bounded open region of the $d$ dimensional space
we consider a Brownian motion which is reborn at a
fixed interior point as soon as it reaches the
boundary. The evolution is invariant with respect to a
density equal, modulo a constant, to the Green function
of the Dirichlet Laplacian centered at the point of
return. We calculate the resolvent in closed form,
study its spectral properties and determine explicitly
the spectrum in dimension one. Two proofs of the
exponential ergodicity are given, one using the inverse
Laplace transform and properties of analytic
semigroups, and the other based on Doeblin's condition.
Both methods admit generalizations to a wide class of
processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Dirichlet Laplacian, Green function, analytic
semigroup, jump diffusion",
}
@Article{Biskup:2007:FCR,
author = "Marek Biskup and Timothy Prescott",
title = "Functional {CLT} for Random Walk Among Bounded Random
Conductances",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "49:1323--49:1348",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-456",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/456",
abstract = "We consider the nearest-neighbor simple random walk on
$ Z^d $, $ d \ge 2 $, driven by a field of i.i.d.
random nearest-neighbor conductances $ \omega_{xy} \in
[0, 1] $. Apart from the requirement that the bonds
with positive conductances percolate, we pose no
restriction on the law of the $ \omega $'s. We prove
that, for a.e. realization of the environment, the path
distribution of the walk converges weakly to that of
non-degenerate, isotropic Brownian motion. The quenched
functional CLT holds despite the fact that the local
CLT may fail in $ d \ge 5 $ due to anomalously slow
decay of the probability that the walk returns to the
starting point at a given time.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Random conductance model, invariance principle,
corrector, homogenization, heat kernel, percolation,
isoperimetry",
}
@Article{Mytnik:2007:LES,
author = "Leonid Mytnik and Jie Xiong",
title = "Local extinction for superprocesses in random
environments",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "50:1349--50:1378",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-457",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/457",
abstract = "We consider a superprocess in a random environment
represented by a random measure which is white in time
and colored in space with correlation kernel $ g(x, y)
$. Suppose that $ g(x, y) $ decays at a rate of $ |x -
y|^{- \alpha } $, $ 0 \leq \alpha \leq 2 $, as $ |x -
y| \to \infty $. We show that the process, starting
from Lebesgue measure, suffers long-term local
extinction. If $ \alpha < 2 $, then it even suffers
finite time local extinction. This property is in
contrast with the classical super-Brownian motion which
has a non-trivial limit when the spatial dimension is
higher than 2. We also show in this paper that in
dimensions $ d = 1, 2 $ superprocess in random
environment suffers local extinction for any bounded
function $g$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Tykesson:2007:NUC,
author = "Johan Tykesson",
title = "The number of unbounded components in the {Poisson}
{Boolean} model of continuum percolation in hyperbolic
space",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "51:1379--51:1401",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-460",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/460",
abstract = "We consider the Poisson Boolean model of continuum
percolation with balls of fixed radius $R$ in
$n$-dimensional hyperbolic space $ H^n$. Let $ \lambda
$ be the intensity of the underlying Poisson process,
and let $ N_C$ denote the number of unbounded
components in the covered region. For the model in any
dimension we show that there are intensities such that
$ N_C = \infty $ a.s. if $R$ is big enough. In $ H^2$
we show a stronger result: for any $R$ there are two
intensities $ \lambda_c$ and $ \lambda_u$ where $ 0 <
\lambda_c < \lambda_u < \infty $, such that$ N_C = 0$
for $ \lambda \in [0, \lambda_c]$, $ N_C = \infty $ for
$ \lambda \in (\lambda_c, \lambda_u)$ and $ N_C = 1$
for $ \lambda \in [\lambda_u, \infty)$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "continuum percolation; hyperbolic space; phase
transitions",
}
@Article{Hu:2007:EES,
author = "Zhishui Hu and John Robinson and Qiying Wang",
title = "{Edgeworth} Expansions for a Sample Sum from a Finite
Set of Independent Random Variables",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "52:1402--52:1417",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-447",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/447",
abstract = "Let $ \{ X_1, \cdots, X_N \} $ be a set of $N$
independent random variables, and let $ S_n$ be a sum
of $n$ random variables chosen without replacement from
the set $ \{ X_1, \cdots, X_N \} $ with equal
probabilities. In this paper we give a one-term
Edgeworth expansion of the remainder term for the
normal approximation of $ S_n$ under mild conditions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Edgeworth expansion, finite population, sampling
without replacement",
}
@Article{Ankirchner:2007:CVD,
author = "Stefan Ankirchner and Peter Imkeller and Goncalo {Dos
Reis}",
title = "Classical and Variational Differentiability of {BSDEs}
with Quadratic Growth",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "53:1418--53:1453",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-462",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/462",
abstract = "We consider Backward Stochastic Differential Equations
(BSDEs) with generators that grow quadratically in the
control variable. In a more abstract setting, we first
allow both the terminal condition and the generator to
depend on a vector parameter $x$. We give sufficient
conditions for the solution pair of the BSDE to be
differentiable in $x$. These results can be applied to
systems of forward--backward SDE. If the terminal
condition of the BSDE is given by a sufficiently smooth
function of the terminal value of a forward SDE, then
its solution pair is differentiable with respect to the
initial vector of the forward equation. Finally we
prove sufficient conditions for solutions of quadratic
BSDEs to be differentiable in the variational sense
(Malliavin differentiable).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "BSDE, forward--backward SDE, quadratic growth,
differentiability, stochastic calculus of variations,
Malliavin calculus, Feynman--Kac formula, BMO
martingale, reverse Holder inequality",
}
@Article{Aldous:2007:PUR,
author = "David Aldous and Russell Lyons",
title = "Processes on Unimodular Random Networks",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "54:1454--54:1508",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-463",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
note = "See errata \cite{Aldous:2017:EPU,Aldous:2019:SEP}.",
URL = "http://ejp.ejpecp.org/article/view/463",
abstract = "We investigate unimodular random networks. Our
motivations include their characterization via
reversibility of an associated random walk and their
similarities to unimodular quasi-transitive graphs. We
extend various theorems concerning random walks,
percolation, spanning forests, and amenability from the
known context of unimodular quasi-transitive graphs to
the more general context of unimodular random networks.
We give properties of a trace associated to unimodular
random networks with applications to stochastic
comparison of continuous-time random walk.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Amenability, equivalence relations, infinite graphs,
percolation, quasi-transitive, random walks,
transitivity, weak convergence, reversibility, trace,
stochastic comparison, spanning forests, sofic groups",
}
@Article{White:2007:PID,
author = "David White",
title = "Processes with inert drift",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "55:1509--55:1546",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-465",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/465",
abstract = "We construct a stochastic process whose drift is a
function of the process's local time at a reflecting
barrier. The process arose as a model of the
interactions of a Brownian particle and an inert
particle in a paper by Knight [7]. We construct and
give asymptotic results for two different arrangements
of inert particles and Brownian particles, and
construct the analogous process in higher dimensions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion; local time; Skorohod lemma",
}
@Article{Gnedin:2007:NCL,
author = "Alexander Gnedin and Yuri Yakubovich",
title = "On the Number of Collisions in Lambda-Coalescents",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "56:1547--56:1567",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-464",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/464",
abstract = "We examine the total number of collisions $ C_n $ in
the $ \Lambda $-coalescent process which starts with
$n$ particles. A linear growth and a stable limit law
for $ C_n$ are shown under the assumption of a
power-like behaviour of the measure $ \Lambda $ near
$0$ with exponent $ 0 < \alpha < 1$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "collisions; Lambda-coalescent; stable limit",
}
@Article{Feng:2007:GIF,
author = "Chunrong Feng and Huaizhong Zhao",
title = "A Generalized {It{\^o}}'s Formula in Two-Dimensions
and Stochastic {Lebesgue--Stieltjes} Integrals",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "57:1568--57:1599",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-468",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/468",
abstract = "In this paper, a generalized It$ {\hat {\rm o}} $'s
formula for continuous functions of two-dimensional
continuous semimartingales is proved. The formula uses
the local time of each coordinate process of the
semimartingale, the left space first derivatives and
the second derivative $ \nabla_1^- \nabla_2^-f $, and
the stochastic Lebesgue--Stieltjes integrals of two
parameters. The second derivative $ \nabla_1^-
\nabla_2^-f $ is only assumed to be of locally bounded
variation in certain variables. Integration by parts
formulae are asserted for the integrals of local times.
The two-parameter integral is defined as a natural
generalization of both the It{\^o} integral and the
Lebesgue--Stieltjes integral through a type of It$
{\hat {\rm o }} $ isometry formula.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "continuous semimartingale; generalized It{\^o}'s
formula; local time; stochastic Lebesgue--Stieltjes
integral",
}
@Article{Janson:2007:TEB,
author = "Svante Janson and Guy Louchard",
title = "Tail estimates for the {Brownian} excursion area and
other {Brownian} areas",
journal = j-ELECTRON-J-PROBAB,
volume = "12",
pages = "58:1600--58:1632",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v12-471",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/471",
abstract = "Brownian areas are considered in this paper: the
Brownian excursion area, the Brownian bridge area, the
Brownian motion area, the Brownian meander area, the
Brownian double meander area, the positive part of
Brownian bridge area, the positive part of Brownian
motion area. We are interested in the asymptotics of
the right tail of their density function. Inverting a
double Laplace transform, we can derive, in a
mechanical way, all terms of an asymptotic expansion.
We illustrate our technique with the computation of the
first four terms. We also obtain asymptotics for the
right tail of the distribution function and for the
moments. Our main tool is the two-dimensional saddle
point method.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian areas, asymptotics for density functions
right tail, double Laplace transform, two-dimensional
saddle point method",
}
@Article{Chaumont:2008:CLP,
author = "Lo{\"\i}c Chaumont and Ronald Doney",
title = "Corrections to {``On L{\'e}vy processes conditioned to
stay positive''}",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "1:1--1:4",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-466",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
note = "See \cite{Chaumont:2005:LPC}.",
URL = "http://ejp.ejpecp.org/article/view/466",
abstract = "We correct two errors of omission in our paper, On
L{\'e}vy processes conditioned to stay positive.
\url{http://www.math.washington.edu/~ejpecp/viewarticle.php?id=1517&layout=abstract}
Electron. J. Probab. {\bf 10}, (2005), no. 28,
948--961. Math. Review 2006h:60079.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "L{\'e}vy process, conditioned to stay positive, weak
convergence, excursion measure",
}
@Article{Kurkova:2008:LES,
author = "Irina Kurkova",
title = "Local Energy Statistics in Directed Polymers",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "2:5--2:25",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-475",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/475",
abstract = "Recently, Bauke and Mertens conjectured that the local
statistics of energies in random spin systems with
discrete spin space should, in most circumstances, be
the same as in the random energy model. We show that
this conjecture holds true as well for directed
polymers in random environment. We also show that,
under certain conditions, this conjecture holds for
directed polymers even if energy levels that grow
moderately with the volume of the system are
considered.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Directed polymers",
}
@Article{Chen:2008:CPE,
author = "Guan-Yu Chen and Laurent Saloff-Coste",
title = "The Cutoff Phenomenon for Ergodic {Markov} Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "3:26--3:78",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-474",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/474",
abstract = "We consider the cutoff phenomenon in the context of
families of ergodic Markov transition functions. This
includes classical examples such as families of ergodic
finite Markov chains and Brownian motion on families of
compact Riemannian manifolds. We give criteria for the
existence of a cutoff when convergence is measured in $
L^p$-norm, $ 1 < p < \infty $. This allows us to prove
the existence of a cutoff in cases where the cutoff
time is not explicitly known. In the reversible case,
for $ 1 < p \leq \infty $, we show that a necessary and
sufficient condition for the existence of a max-$ L^p$
cutoff is that the product of the spectral gap by the
max-$ L^p$ mixing time tends to infinity. This type of
condition was suggested by Yuval Peres. Illustrative
examples are discussed.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "cutoff phenomenon, ergodic Markov semigroups",
}
@Article{Miermont:2008:RPR,
author = "Gr{\'e}gory Miermont and Mathilde Weill",
title = "Radius and profile of random planar maps with faces of
arbitrary degrees",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "4:79--4:106",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-478",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/478",
abstract = "We prove some asymptotic results for the radius and
the profile of large random planar maps with faces of
arbitrary degrees. Using a bijection due to Bouttier,
Di Francesco \& Guitter between rooted planar maps and
certain four-type trees with positive labels, we derive
our results from a conditional limit theorem for
four-type spatial Galton--Watson trees.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian snake; invariance principle; multitype
spatial Galton--Watson tree; Random planar map",
}
@Article{Houdre:2008:CSM,
author = "Christian Houdr{\'e} and Hua Xu",
title = "Concentration of the Spectral Measure for Large Random
Matrices with Stable Entries",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "5:107--5:134",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-482",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/482",
abstract = "We derive concentration inequalities for functions of
the empirical measure of large random matrices with
infinitely divisible entries, in particular, stable or
heavy tails ones. We also give concentration results
for some other functionals of these random matrices,
such as the largest eigenvalue or the largest singular
value.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Spectral Measure, Random Matrices, Infinitely
divisibility, Stable Vector, Concentration",
}
@Article{Fournier:2008:SLS,
author = "Nicolas Fournier",
title = "Smoothness of the law of some one-dimensional jumping
S.D.E.s with non-constant rate of jump",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "6:135--6:156",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-480",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/480",
abstract = "We consider a one-dimensional jumping Markov process,
solving a Poisson-driven stochastic differential
equation. We prove that the law of this process admits
a smooth density for all positive times, under some
regularity and non-degeneracy assumptions on the
coefficients of the S.D.E. To our knowledge, our result
is the first one including the important case of a
non-constant rate of jump. The main difficulty is that
in such a case, the process is not smooth as a function
of its initial condition. This seems to make impossible
the use of Malliavin calculus techniques. To overcome
this problem, we introduce a new method, in which the
propagation of the smoothness of the density is
obtained by analytic arguments.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic differential equations, Jump processes,
Regularity of the density",
}
@Article{Savov:2008:CCR,
author = "Mladen Savov",
title = "Curve Crossing for the Reflected {L{\'e}vy} Process at
Zero and Infinity",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "7:157--7:172",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-483",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/483",
abstract = "Let $ R_t = \sup_{0 \leq s \leq t}X_s - X_t $ be a
Levy process reflected in its maximum. We give
necessary and sufficient conditions for finiteness of
passage times above power law boundaries at infinity.
Information as to when the expected passage time for $
R_t $ is finite, is given. We also discuss the almost
sure finiteness of $ \limsup_{t \to 0}R_t / t^{\kappa }
$, for each $ \kappa \geq 0 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Reflected process, passage times, power law
boundaries",
}
@Article{Baurdoux:2008:MSG,
author = "Erik Baurdoux and Andreas Kyprianou",
title = "The {McKean} stochastic game driven by a spectrally
negative {L{\'e}vy} process",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "8:173--8:197",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-484",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/484",
abstract = "We consider the stochastic-game-analogue of McKean's
optimal stopping problem when the underlying source of
randomness is a spectrally negative L{\'e}vy process.
Compared to the solution for linear Brownian motion
given in Kyprianou (2004) one finds two new phenomena.
Firstly the breakdown of smooth fit and secondly the
stopping domain for one of the players `thickens' from
a singleton to an interval, at least in the case that
there is no Gaussian component.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic games, optimal stopping, pasting
principles, fluctuation theory, L'evy processes",
}
@Article{Fill:2008:TPK,
author = "James Fill and David Wilson",
title = "Two-Player Knock 'em Down",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "9:198--9:212",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-485",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/485",
abstract = "We analyze the two-player game of Knock 'em Down,
asymptotically as the number of tokens to be knocked
down becomes large. Optimal play requires mixed
strategies with deviations of order $ \sqrt {n} $ from
the na{\"\i}ve law-of-large numbers allocation. Upon
rescaling by $ \sqrt {n} $ and sending $ n \to \infty
$, we show that optimal play's random deviations always
have bounded support and have marginal distributions
that are absolutely continuous with respect to Lebesgue
measure.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "game theory; Knock 'em Down; Nash equilibrium",
}
@Article{Caputo:2008:AEP,
author = "Pietro Caputo and Fabio Martinelli and Fabio
Toninelli",
title = "On the Approach to Equilibrium for a Polymer with
Adsorption and Repulsion",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "10:213--10:258",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-486",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/486",
abstract = "We consider paths of a one-dimensional simple random
walk conditioned to come back to the origin after $L$
steps, $ L \in 2 \mathbb {N}$. In the {\em pinning
model} each path $ \eta $ has a weight $
\lambda^{N(\eta)}$, where $ \lambda > 0$ and $ N(\eta)$
is the number of zeros in $ \eta $. When the paths are
constrained to be non-negative, the polymer is said to
satisfy a hard-wall constraint. Such models are well
known to undergo a localization/delocalization
transition as the pinning strength $ \lambda $ is
varied. In this paper we study a natural ``spin flip''
dynamics for associated to these models and derive
several estimates on its spectral gap and mixing time.
In particular, for the system with the wall we prove
that relaxation to equilibrium is always at least as
fast as in the free case (i.e., $ \lambda = 1$ without
the wall), where the gap and the mixing time are known
to scale as $ L^{-2}$ and $ L^2 \log L$, respectively.
This improves considerably over previously known
results. For the system without the wall we show that
the equilibrium phase transition has a clear dynamical
manifestation: for $ \lambda \geq 1$ relaxation is
again at least as fast as the diffusive free case, but
in the strictly delocalized phase ($ \lambda < 1$) the
gap is shown to be $ O(L^{-5 / 2})$, up to logarithmic
corrections. As an application of our bounds, we prove
stretched exponential relaxation of local functions in
the localized regime.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Coupling; Dynamical phase transition; Mixing time;
Pinning model; Spectral gap",
}
@Article{Davydov:2008:SSD,
author = "Youri Davydov and Ilya Molchanov and Sergei Zuyev",
title = "Strictly stable distributions on convex cones",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "11:259--11:321",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-487",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/487",
abstract = "Using the LePage representation, a symmetric
alpha-stable random element in Banach space B with
alpha from (0, 2) can be represented as a sum of points
of a Poisson process in B. This point process is
union-stable, i.e., the union of its two independent
copies coincides in distribution with the rescaled
original point process. This shows that the classical
definition of stable random elements is closely related
to the union-stability property of point processes.
These concepts make sense in any convex cone, i.e., in
a semigroup equipped with multiplication by numbers,
and lead to a construction of stable laws in general
cones by means of the LePage series. We prove that
random samples (or binomial point processes) in rather
general cones converge in distribution in the vague
topology to the union-stable Poisson point process.
This convergence holds also in a stronger topology,
which implies that the sums of points converge in
distribution to the sum of points of the union-stable
point process. Since the latter corresponds to a stable
law, this yields a limit theorem for normalised sums of
random elements with alpha-stable limit for alpha from
(0, 1). By using the technique of harmonic analysis on
semigroups we characterise distributions of
alpha-stable random elements and show how possible
values of the characteristic exponent alpha relate to
the properties of the semigroup and the corresponding
scaling operation, in particular, their distributivity
properties. It is shown that several conditions imply
that a stable random element admits the LePage
representation. The approach developed in the paper not
only makes it possible to handle stable distributions
in rather general cones (like spaces of sets or
measures), but also provides an alternative way to
prove classical limit theorems and deduce the LePage
representation for strictly stable random vectors in
Banach spaces.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "character; convex cone; Laplace transform; LePage
series; L{\'e}vy measure; point process; Poisson
process; random measure; random set; semigroup; stable
distribution; union-stability",
}
@Article{Merlet:2008:CTS,
author = "Glenn Merlet",
title = "Cycle time of stochastic max-plus linear systems",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "12:322--12:340",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-488",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/488",
abstract = "We analyze the asymptotic behavior of sequences of
random variables defined by an initial condition, a
stationary and ergodic sequence of random matrices, and
an induction formula involving multiplication is the
so-called max-plus algebra. This type of recursive
sequences are frequently used in applied probability as
they model many systems as some queueing networks,
train and computer networks, and production systems. We
give a necessary condition for the recursive sequences
to satisfy a strong law of large numbers, which proves
to be sufficient when the matrices are i.i.d. Moreover,
we construct a new example, in which the sequence of
matrices is strongly mixing, that condition is
satisfied, but the recursive sequence do not converges
almost surely.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "law of large numbers; Markov chains; max-plus;
products of random matrices; stochastic recursive
sequences; subadditivity",
}
@Article{Lamberton:2008:PBA,
author = "Damien Lamberton and Gilles Pag{\`e}s",
title = "A penalized bandit algorithm",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "13:341--13:373",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-489",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/489",
abstract = "We study a two armed-bandit recursive algorithm with
penalty. We show that the algorithm converges towards
its ``target'' although it always has a noiseless
``trap''. Then, we elucidate the rate of convergence.
For some choices of the parameters, we obtain a central
limit theorem in which the limit distribution is
characterized as the unique stationary distribution of
a Markov process with jumps.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "convergence rate; learning; penalization; stochastic
approximation; Two-armed bandit algorithm",
}
@Article{Berestycki:2008:LBD,
author = "Nathanael Berestycki and Rick Durrett",
title = "Limiting behavior for the distance of a random walk",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "14:374--14:395",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-490",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/490",
abstract = "In this paper we study some aspects of the behavior of
random walks on large but finite graphs before they
have reached their equilibrium distribution. This
investigation is motivated by a result we proved
recently for the random transposition random walk: the
distance from the starting point of the walk has a
phase transition from a linear regime to a sublinear
regime at time $ n / 2 $. Here, we study the examples
of random 3-regular graphs, random adjacent
transpositions, and riffle shuffles. In the case of a
random 3-regular graph, there is a phase transition
where the speed changes from 1/3 to 0 at time $ 3 l o
g_2 n $. A similar result is proved for riffle
shuffles, where the speed changes from 1 to 0 at time $
l o g_2 n $. Both these changes occur when a distance
equal to the average diameter of the graph is reached.
However in the case of random adjacent transpositions,
the behavior is more complex. We find that there is no
phase transition, even though the distance has
different scalings in three different regimes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "random walk, phase transition, adjacent
transpositions, random regular graphs, riffle
shuffles",
}
@Article{Lember:2008:IRR,
author = "Jyri Lember and Heinrich Matzinger",
title = "Information recovery from randomly mixed-up message
text",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "15:396--15:466",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-491",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/491",
abstract = "This paper is concerned with finding a fingerprint of
a sequence. As input data one uses the sequence which
has been randomly mixed up by observing it along a
random walk path. A sequence containing order exp (n)
bits receives a fingerprint with roughly n bits
information. The fingerprint is characteristic for the
original sequence. With high probability the
fingerprint depends only on the initial sequence, but
not on the random walk path.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "random walk in random environment; Scenery
reconstruction",
}
@Article{Beghin:2008:PPG,
author = "Luisa Beghin",
title = "Pseudo-Processes Governed by Higher-Order Fractional
Differential Equations",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "16:467--16:485",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-496",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/496",
abstract = "We study here a heat-type differential equation of
order $n$ greater than two, in the case where the
time-derivative is supposed to be fractional. The
corresponding solution can be described as the
transition function of a pseudoprocess $ \Psi_n$
(coinciding with the one governed by the standard,
non-fractional, equation) with a time argument $
\mathcal {T}_{\alpha }$ which is itself random. The
distribution of $ \mathcal {T}_{\alpha }$ is presented
together with some features of the solution (such as
analytic expressions for its moments).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Fractional derivatives; Higher-order heat-type
equations; Stable laws.; Wright functions",
}
@Article{Basdevant:2008:AAF,
author = "Anne-Laure Basdevant and Christina Goldschmidt",
title = "Asymptotics of the Allele Frequency Spectrum
Associated with the {Bolthausen--Sznitman} Coalescent",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "17:486--17:512",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-494",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/494",
abstract = "We consider a coalescent process as a model for the
genealogy of a sample from a population. The population
is subject to neutral mutation at constant rate $ \rho
$ per individual and every mutation gives rise to a
completely new type. The allelic partition is obtained
by tracing back to the most recent mutation for each
individual and grouping together individuals whose most
recent mutations are the same. The allele frequency
spectrum is the sequence $ (N_1 (n), N_2 (n), \ldots,
N_n(n)) $, where $ N_k(n) $ is number of blocks of size
$k$ in the allelic partition with sample size $n$. In
this paper, we prove law of large numbers-type results
for the allele frequency spectrum when the coalescent
process is taken to be the Bolthausen--Sznitman
coalescent. In particular, we show that $ n^{-1}(\log
n) N_1 (n) {\stackrel {p}{\rightarrow }} \rho $ and,
for $ k \geq 2$, $ n^{-1}(\log n)^2 N_k(n) {\stackrel
{p}{\rightarrow }} \rho / (k(k - 1))$ as $ n \to \infty
$. Our method of proof involves tracking the formation
of the allelic partition using a certain Markov
process, for which we prove a fluid limit.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Giacomin:2008:RCR,
author = "Giambattista Giacomin",
title = "Renewal convergence rates and correlation decay for
homogeneous pinning models",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "18:513--18:529",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-497",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/497",
abstract = "A class of discrete renewal processes with
exponentially decaying inter-arrival distributions
coincides with the infinite volume limit of general
homogeneous pinning models in their localized phase.
Pinning models are statistical mechanics systems to
which a lot of attention has been devoted both for
their relevance for applications and because they are
solvable models exhibiting a non-trivial phase
transition. The spatial decay of correlations in these
systems is directly mapped to the speed of convergence
to equilibrium for the associated renewal processes. We
show that close to criticality, under general
assumptions, the correlation decay rate, or the renewal
convergence rate, coincides with the inter-arrival
decay rate. We also show that, in general, this is
false away from criticality. Under a stronger
assumption on the inter-arrival distribution we
establish a local limit theorem, capturing thus the
sharp asymptotic behavior of correlations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Criticality; Decay of Correlations; Exponential Tails;
Pinning Models; Renewal Theory; Speed of Convergence to
Equilibrium",
}
@Article{Merkl:2008:BRE,
author = "Franz Merkl and Silke Rolles",
title = "Bounding a Random Environment Bounding a Random
Environment for Two-dimensional Edge-reinforced Random
Walk",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "19:530--19:565",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-495",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/495",
abstract = "We consider edge-reinforced random walk on the
infinite two-dimensional lattice. The process has the
same distribution as a random walk in a certain
strongly dependent random environment, which can be
described by random weights on the edges. In this
paper, we show some decay properties of these random
weights. Using these estimates, we derive bounds for
some hitting probabilities of the edge-reinforced
random walk.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "random environment; Reinforced random walk",
}
@Article{Daly:2008:UBS,
author = "Fraser Daly",
title = "Upper Bounds for {Stein}-Type Operators",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "20:566--20:587",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-479",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/479",
abstract = "We present sharp bounds on the supremum norm of $
\mathcal {D}^j S h $ for $ j \geq 2 $, where $ \mathcal
{D} $ is the differential operator and $S$ the Stein
operator for the standard normal distribution. The same
method is used to give analogous bounds for the
exponential, Poisson and geometric distributions, with
$ \mathcal {D}$ replaced by the forward difference
operator in the discrete case. We also discuss
applications of these bounds to the central limit
theorem, simple random sampling, Poisson--Charlier
approximation and geometric approximation using
stochastic orderings.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "central limit theorem; Poisson--Charlier
approximation; Stein's method; Stein-type operator;
stochastic ordering",
}
@Article{Bose:2008:ALM,
author = "Arup Bose and Arnab Sen",
title = "Another look at the moment method for large
dimensional random matrices",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "21:588--21:628",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-501",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/501",
abstract = "The methods to establish the limiting spectral
distribution (LSD) of large dimensional random matrices
includes the well known moment method which invokes the
trace formula. Its success has been demonstrated in
several types of matrices such as the Wigner matrix and
the sample variance covariance matrix. In a recent
article Bryc, Dembo and Jiang (2006) establish the LSD
for the random Toeplitz and Hankel matrices using the
moment method. They perform the necessary counting of
terms in the trace by splitting the relevant sets into
equivalent classes and relating the limits of the
counts to certain volume calculations.\par
We build on their work and present a unified approach.
This helps provide relatively short and easy proofs for
the LSD of common matrices while at the same time
providing insight into the nature of different LSD and
their interrelations. By extending these methods we are
also able to deal with matrices with appropriate
dependent entries.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Bounded Lipschitz metric, large dimensional random
matrices, eigenvalues, Wigner matrix, sample variance
covariance matrix, Toeplitz matrix, Hankel matrix,
circulant matrix, symmetric circulant matrix, reverse
circulant matrix, palindromic matrix, limit",
}
@Article{Conus:2008:NLS,
author = "Daniel Conus and Robert Dalang",
title = "The Non-Linear Stochastic Wave Equation in High
Dimensions",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "22:629--22:670",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-500",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/500",
abstract = "We propose an extension of Walsh's classical
martingale measure stochastic integral that makes it
possible to integrate a general class of Schwartz
distributions, which contains the fundamental solution
of the wave equation, even in dimensions greater than
3. This leads to a square-integrable random-field
solution to the non-linear stochastic wave equation in
any dimension, in the case of a driving noise that is
white in time and correlated in space. In the
particular case of an affine multiplicative noise, we
obtain estimates on $p$-th moments of the solution ($ p
\geq 1$), and we show that the solution is H{\"o}lder
continuous. The H{\"o}lder exponent that we obtain is
optimal.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "H{\"o}lder continuity; Martingale measures; moment
formulae; stochastic integration; stochastic partial
differential equations; stochastic wave equation",
}
@Article{Holmes:2008:CLT,
author = "Mark Holmes",
title = "Convergence of Lattice Trees to Super-{Brownian}
Motion above the Critical Dimension",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "23:671--23:755",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-499",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/499",
abstract = "We use the lace expansion to prove asymptotic formulae
for the Fourier transforms of the $r$-point functions
for a spread-out model of critically weighted lattice
trees on the $d$-dimensional integer lattice for $ d >
8$. A lattice tree containing the origin defines a
sequence of measures on the lattice, and the
statistical mechanics literature gives rise to a
natural probability measure on the collection of such
lattice trees. Under this probability measure, our
results, together with the appropriate limiting
behaviour for the survival probability, imply
convergence to super-Brownian excursion in the sense of
finite-dimensional distributions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "lace expansion.; Lattice trees; super-Brownian
motion",
}
@Article{Roellin:2008:SCB,
author = "Adrian Roellin",
title = "Symmetric and centered binomial approximation of sums
of locally dependent random variables",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "24:756--24:776",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-503",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/503",
abstract = "Stein's method is used to approximate sums of discrete
and locally dependent random variables by a centered
and symmetric binomial distribution, serving as a
natural alternative to the normal distribution in
discrete settings. The bounds are given with respect to
the total variation and a local limit metric. Under
appropriate smoothness properties of the summands, the
same order of accuracy as in the Berry--Ess{\'e}en
Theorem is achieved. The approximation of the total
number of points of a point processes is also
considered. The results are applied to the exceedances
of the $r$-scans process and to the Mat{\'e}rn hardcore
point process type I to obtain explicit bounds with
respect to the two metrics.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "binomial distribution; local dependence; Stein's
method; total variation metric",
}
@Article{Champagnat:2008:LTC,
author = "Nicolas Champagnat and Sylvie Roelly",
title = "Limit theorems for conditioned multitype
{Dawson--Watanabe} processes and {Feller} diffusions",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "25:777--25:810",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-504",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/504",
abstract = "A multitype Dawson--Watanabe process is conditioned,
in subcritical and critical cases, on non-extinction in
the remote future. On every finite time interval, its
distribution is absolutely continuous with respect to
the law of the unconditioned process. A martingale
problem characterization is also given. Several results
on the long time behavior of the conditioned mass
process-the conditioned multitype Feller branching
diffusion-are then proved. The general case is first
considered, where the mutation matrix which models the
interaction between the types, is irreducible. Several
two-type models with decomposable mutation matrices are
analyzed too.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "conditioned Dawson--Watanabe process; conditioned
Feller diffusion; critical and subcritical
Dawson--Watanabe process; long time behavior.;
multitype measure-valued branching processes; remote
survival",
}
@Article{Basdevant:2008:RGT,
author = "Anne-Laure Basdevant and Arvind Singh",
title = "Rate of growth of a transient cookie random walk",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "26:811--26:851",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-498",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/498",
abstract = "We consider a one-dimensional transient cookie random
walk. It is known from a previous paper (BS2008) that a
cookie random walk $ (X_n) $ has positive or zero speed
according to some positive parameter $ \alpha > 1 $ or
$ \leq 1 $. In this article, we give the exact rate of
growth of $ X_n $ in the zero speed regime, namely: for
$ 0 < \alpha < 1 $, $ X_n / n^{(? + 1) / 2} $ converges
in law to a Mittag-Leffler distribution whereas for $
\alpha = 1 $, $ X_n(\log n) / n $ converges in
probability to some positive constant.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "branching process with migration; cookie or
multi-excited random walk; Rates of transience",
}
@Article{Petrou:2008:MCL,
author = "Evangelia Petrou",
title = "{Malliavin} Calculus in {L{\'e}vy} spaces and
Applications to Finance",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "27:852--27:879",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-502",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/502",
abstract = "The main goal of this paper is to generalize the
results of Fournie et al. [7] for markets generated by
L{\'e}vy processes. For this reason we extend the
theory of Malliavin calculus to provide the tools that
are necessary for the calculation of the sensitivities,
such as differentiability results for the solution of a
stochastic differential equation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Windisch:2008:LCV,
author = "David Windisch",
title = "Logarithmic Components of the Vacant Set for Random
Walk on a Discrete Torus",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "28:880--28:897",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-506",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/506",
abstract = "This work continues the investigation, initiated in a
recent work by Benjamini and Sznitman, of percolative
properties of the set of points not visited by a random
walk on the discrete torus $ ({\mathbb Z} / N{\mathbb
Z})^d $ up to time $ u N^d $ in high dimension $d$. If
$ u > 0$ is chosen sufficiently small it has been shown
that with overwhelming probability this vacant set
contains a unique giant component containing segments
of length $ c_0 \log N$ for some constant $ c_0 > 0$,
and this component occupies a non-degenerate fraction
of the total volume as $N$ tends to infinity. Within
the same setup, we investigate here the complement of
the giant component in the vacant set and show that
some components consist of segments of logarithmic
size. In particular, this shows that the choice of a
sufficiently large constant $ c_0 > 0$ is crucial in
the definition of the giant component.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "discrete torus; Giant component; random walk; vacant
set",
}
@Article{Boufoussi:2008:PPC,
author = "Brahim Boufoussi and Marco Dozzi and Raby Guerbaz",
title = "Path properties of a class of locally asymptotically
self similar processes",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "29:898--29:921",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-505",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/505",
abstract = "Various paths properties of a stochastic process are
obtained under mild conditions which allow for the
integrability of the characteristic function of its
increments and for the dependence among them. The main
assumption is closely related to the notion of local
asymptotic self-similarity. New results are obtained
for the class of multifractional random processes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Hausdorff dimension, level sets, local asymptotic
self-similarity, local non-determinism, local times",
}
@Article{Reynolds:2008:DRS,
author = "David Reynolds and John Appleby",
title = "Decay Rates of Solutions of Linear Stochastic
{Volterra} Equations",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "30:922--30:943",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-507",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/507",
abstract = "The paper studies the exponential and non--exponential
convergence rate to zero of solutions of scalar linear
convolution It{\^o}-Volterra equations in which the
noise intensity depends linearly on the current state.
By exploiting the positivity of the solution, various
upper and lower bounds in first mean and almost sure
sense are obtained, including Liapunov exponents.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "almost sure exponential asymptotic stability, Liapunov
exponent, subexponential distribution, subexponential
function, Volterra equations, It{\^o}-Volterra
equations",
}
@Article{Menshikov:2008:URR,
author = "Mikhail Menshikov and Stanislav Volkov",
title = "Urn-related random walk with drift $ \rho x^\alpha /
t^\beta $",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "31:944--31:960",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-508",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/508",
abstract = "We study a one-dimensional random walk whose expected
drift depends both on time and the position of a
particle. We establish a non-trivial phase transition
for the recurrence vs. transience of the walk, and show
some interesting applications to Friedman's urn, as
well as showing the connection with Lamperti's walk
with asymptotically zero drift.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "martingales; Random walks; urn models",
}
@Article{Kulik:2008:SEV,
author = "Rafal Kulik",
title = "Sums of extreme values of subordinated long-range
dependent sequences: moving averages with finite
variance",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "32:961--32:979",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-510",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/510",
abstract = "In this paper we study the limiting behavior of sums
of extreme values of long range dependent sequences
defined as functionals of linear processes with finite
variance. If the number of extremes in a sum is large
enough, we obtain asymptotic normality, however, the
scaling factor is relatively bigger than in the i.i.d
case, meaning that the maximal terms have relatively
smaller contribution to the whole sum. Also, it is
possible for a particular choice of a model, that the
scaling need not to depend on the tail index of the
underlying marginal distribution, as it is well-known
to be so in the i.i.d. situation. Furthermore,
subordination may change the asymptotic properties of
sums of extremes.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "sample quantiles, linear processes, empirical
processes, long range dependence, sums of extremes,
trimmed sums",
}
@Article{Broman:2008:LLC,
author = "Erik Broman and Federico Camia",
title = "Large-{$N$} Limit of Crossing Probabilities,
Discontinuity, and Asymptotic Behavior of Threshold
Values in {Mandelbrot}'s Fractal Percolation Process",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "33:980--33:999",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-511",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/511",
abstract = "We study Mandelbrot's percolation process in dimension
$ d \geq 2 $. The process generates random fractal sets
by an iterative procedure which starts by dividing the
unit cube $ [0, 1]^d $ in $ N^d $ subcubes, and
independently retaining or discarding each subcube with
probability $p$ or $ 1 - p$ respectively. This step is
then repeated within the retained subcubes at all
scales. As $p$ is varied, there is a percolation phase
transition in terms of paths for all $ d \geq 2$, and
in terms of $ (d - 1)$-dimensional ``sheets'' for all $
d \geq 3$.\par
For any $ d \geq 2$, we consider the random fractal set
produced at the path-percolation critical value $
p_c(N, d)$, and show that the probability that it
contains a path connecting two opposite faces of the
cube $ [0, 1]^d$ tends to one as $ N \to \infty $. As
an immediate consequence, we obtain that the above
probability has a discontinuity, as a function of $p$,
at $ p_c(N, d)$ for all $N$ sufficiently large. This
had previously been proved only for $ d = 2$ (for any $
N \geq 2$). For $ d \geq 3$, we prove analogous results
for sheet-percolation.\par
In dimension two, Chayes and Chayes proved that $
p_c(N, 2)$ converges, as $ N \to \infty $, to the
critical density $ p_c$ of site percolation on the
square lattice. Assuming the existence of the
correlation length exponent $ \nu $ for site
percolation on the square lattice, we establish the
speed of convergence up to a logarithmic factor. In
particular, our results imply that $ p_c(N, 2) - p_c =
(\frac {1}{N})^{1 / \nu + o(1)}$ as $ N \to \infty $,
showing an interesting relation with near-critical
percolation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "critical probability; crossing probability;
enhancement/diminishment percolation; Fractal
percolation; near-critical percolation",
}
@Article{Adamczak:2008:TIS,
author = "Radoslaw Adamczak",
title = "A tail inequality for suprema of unbounded empirical
processes with applications to {Markov} chains",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "34:1000--34:1034",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-521",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/521",
abstract = "We present a tail inequality for suprema of empirical
processes generated by variables with finite $
\psi_\alpha $ norms and apply it to some geometrically
ergodic Markov chains to derive similar estimates for
empirical processes of such chains, generated by
bounded functions. We also obtain a bounded difference
inequality for symmetric statistics of such Markov
chains.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "concentration inequalities, empirical processes,
Markov chains",
}
@Article{Matoussi:2008:SSS,
author = "Anis Matoussi and Mingyu Xu",
title = "{Sobolev} solution for semilinear {PDE} with obstacle
under monotonicity condition",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "35:1035--35:1067",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-522",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/522",
abstract = "We prove the existence and uniqueness of Sobolev
solution of a semilinear PDE's and PDE's with obstacle
under monotonicity condition. Moreover we give the
probabilistic interpretation of the solutions in term
of Backward SDE and reflected Backward SDE
respectively",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Backward stochastic differential equation, Reflected
backward stochastic differential equation, monotonicity
condition, Stochastic flow, partial differential
equation with obstacle",
}
@Article{DeBlassie:2008:EPB,
author = "Dante DeBlassie",
title = "The Exit Place of {Brownian} Motion in the Complement
of a Horn",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "36:1068--36:1095",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-524",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/524",
abstract = "Consider the domain lying outside a horn. We determine
asymptotics of the logarithm of the chance that
Brownian motion in the domain has a large exit place.
For a certain class of horns, the behavior is given
explicitly in terms of the geometry of the domain. We
show that for some horns the behavior depends on the
dimension, whereas for other horns, it does not.
Analytically, the result is equivalent to estimating
the harmonic measure of the part of the domain lying
outside a cylinder with large diameter.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Horn-shaped domain, $h$-transform, Feynman--Kac
representation, exit place of Brownian motion, harmonic
measure",
}
@Article{Zambotti:2008:CEB,
author = "Lorenzo Zambotti",
title = "A conservative evolution of the {Brownian} excursion",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "37:1096--37:1119",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-525",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/525",
abstract = "We consider the problem of conditioning the Brownian
excursion to have a fixed time average over the
interval [0, 1] and we study an associated stochastic
partial differential equation with reflection at 0 and
with the constraint of conservation of the space
average. The equation is driven by the derivative in
space of a space-time white noise and contains a double
Laplacian in the drift. Due to the lack of the maximum
principle for the double Laplacian, the standard
techniques based on the penalization method do not
yield existence of a solution.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian excursion; Brownian meander; singular
conditioning; Stochastic partial differential equations
with reflection",
}
@Article{Baudoin:2008:SSF,
author = "Fabrice Baudoin and Laure Coutin",
title = "Self-similarity and fractional {Brownian} motion on
{Lie} groups",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "38:1120--38:1139",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-530",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/530",
abstract = "The goal of this paper is to define and study a notion
of fractional Brownian motion on a Lie group. We define
it as at the solution of a stochastic differential
equation driven by a linear fractional Brownian motion.
We show that this process has stationary increments and
satisfies a local self-similar property. Furthermore
the Lie groups for which this self-similar property is
global are characterized.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Fractional Brownian motion, Lie group",
}
@Article{Basse:2008:GMA,
author = "Andreas Basse",
title = "{Gaussian} Moving Averages and Semimartingales",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "39:1140--39:1165",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-526",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/526",
abstract = "In the present paper we study moving averages (also
known as stochastic convolutions) driven by a Wiener
process and with a deterministic kernel. Necessary and
sufficient conditions on the kernel are provided for
the moving average to be a semimartingale in its
natural filtration. Our results are constructive -
meaning that they provide a simple method to obtain
kernels for which the moving average is a
semimartingale or a Wiener process. Several examples
are considered. In the last part of the paper we study
general Gaussian processes with stationary increments.
We provide necessary and sufficient conditions on
spectral measure for the process to be a
semimartingale.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Gaussian processes; moving averages; non-canonical
representations; semimartingales; stationary processes;
stochastic convolutions",
}
@Article{Alberts:2008:HDS,
author = "Tom Alberts and Scott Sheffield",
title = "{Hausdorff} Dimension of the {SLE} Curve Intersected
with the Real Line",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "40:1166--40:1188",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-515",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/515",
abstract = "We establish an upper bound on the asymptotic
probability of an $ S L E(\kappa) $ curve hitting two
small intervals on the real line as the interval width
goes to zero, for the range $ 4 < \kappa < 8 $. As a
consequence we are able to prove that the random set of
points in $R$ hit by the curve has Hausdorff dimension
$ 2 - 8 / \kappa $, almost surely.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Hausdorff dimension; SLE; Two-point hitting
probability",
}
@Article{Muller:2008:CTM,
author = "Sebastian M{\"u}ller",
title = "A criterion for transience of multidimensional
branching random walk in random environment",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "41:1189--41:1202",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-517",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/517",
abstract = "We develop a criterion for transience for a general
model of branching Markov chains. In the case of
multi-dimensional branching random walk in random
environment (BRWRE) this criterion becomes explicit. In
particular, we show that Condition L of Comets and
Popov [3] is necessary and sufficient for transience as
conjectured. Furthermore, the criterion applies to two
important classes of branching random walks and implies
that the critical branching random walk is transient
resp. dies out locally.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Branching Markov chains; random environment, spectral
radius; recurrence; transience",
}
@Article{Cox:2008:CMW,
author = "Alexander Cox and Jan Obloj",
title = "Classes of measures which can be embedded in the
Simple Symmetric Random Walk",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "42:1203--42:1228",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-516",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/516",
abstract = "We characterize the possible distributions of a
stopped simple symmetric random walk $ X_\tau $, where
$ \tau $ is a stopping time relative to the natural
filtration of $ (X_n) $. We prove that any probability
measure on $ \mathbb {Z} $ can be achieved as the law
of $ X_\tau $ where $ \tau $ is a minimal stopping
time, but the set of measures obtained under the
further assumption that $ (X_{n \land \tau } \colon n
\geq 0) $ is a uniformly integrable martingale is a
fractal subset of the set of all centered probability
measures on $ \mathbb {Z} $. This is in sharp contrast
to the well-studied Brownian motion setting. We also
investigate the discrete counterparts of the
Chacon-Walsh (1976) and Azema-Yor (1979) embeddings and
show that they lead to yet smaller sets of achievable
measures. Finally, we solve explicitly the Skorokhod
embedding problem constructing, for a given measure $
\mu $, a minimal stopping time $ \tau $ which embeds $
\mu $ and which further is uniformly integrable
whenever a uniformly integrable embedding of $ \mu $
exists.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Azema-Yor stopping time; Chacon-Walsh stopping time;
fractal; iterated function system; minimal stopping
time; random walk; self-similar set; Skorokhod
embedding problem; uniform integrability",
}
@Article{Nourdin:2008:WPV,
author = "Ivan Nourdin and Giovanni Peccati",
title = "Weighted power variations of iterated {Brownian}
motion",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "43:1229--43:1256",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-534",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/534",
abstract = "We characterize the asymptotic behaviour of the
weighted power variation processes associated with
iterated Brownian motion. We prove weak convergence
results in the sense of finite dimensional
distributions, and show that the laws of the limiting
objects can always be expressed in terms of three
independent Brownian motions $ X, Y $ and $B$, as well
as of the local times of $Y$. In particular, our
results involve ''weighted'' versions of Kesten and
Spitzer's Brownian motion in random scenery. Our
findings extend the theory initiated by Khoshnevisan
and Lewis (1999), and should be compared with the
recent result by Nourdin and R{\'e}veillac (2008),
concerning the weighted power variations of fractional
Brownian motion with Hurst index $ H = 1 / 4$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion; Brownian motion in random scenery;
Iterated Brownian motion; Limit theorems; Weighted
power variations",
}
@Article{Gibson:2008:MSV,
author = "Lee Gibson",
title = "The mass of sites visited by a random walk on an
infinite graph",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "44:1257--44:1282",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-531",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/531",
abstract = "We determine the log-asymptotic decay rate of the
negative exponential moments of the mass of sites
visited by a random walk on an infinite graph which
satisfies a two-sided sub-Gaussian estimate on its
transition kernel. This provides a new method of proof
of the correct decay rate for Cayley graphs of finitely
generated groups with polynomial volume growth. This
method also extend known results by determining this
decay rate for certain graphs with fractal-like
structure or with non-Alfors regular volume growth
functions.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "random walk, infinite graph, visited sites, asymptotic
decay rates, polynomial volume growth, Cayley graph,
fractal graph, Alfors regular",
}
@Article{Davies:2008:SAN,
author = "Ian Davies",
title = "Semiclassical Analysis and a New Result for
{Poisson--L{\'e}vy} Excursion Measures",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "45:1283--45:1306",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-513",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/513",
abstract = "The Poisson--L{\'e}vy excursion measure for the
diffusion process with small noise satisfying the
It{\^o} equation\par
$$ d X^{\varepsilon } = b(X^{\varepsilon }(t))d t +
\sqrt \varepsilon \, d B(t) $$
is studied and the asymptotic behaviour in $
\varepsilon $ is investigated. The leading order term
is obtained exactly and it is shown that at an
equilibrium point there are only two possible forms for
this term --- Levy or Hawkes--Truman. We also compute
the next to leading order.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "excursion measures, asymptotic expansions",
}
@Article{Eichelsbacher:2008:ORW,
author = "Peter Eichelsbacher and Wolfgang K{\"o}nig",
title = "Ordered Random Walks",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "46:1307--46:1336",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-539",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/539",
abstract = "We construct the conditional version of $k$
independent and identically distributed random walks on
$R$ given that they stay in strict order at all times.
This is a generalisation of so-called non-colliding or
non-intersecting random walks, the discrete variant of
Dyson's Brownian motions, which have been considered
yet only for nearest-neighbor walks on the lattice. Our
only assumptions are moment conditions on the steps and
the validity of the local central limit theorem. The
conditional process is constructed as a Doob
$h$-transform with some positive regular function $V$
that is strongly related with the Vandermonde
determinant and reduces to that function for simple
random walk. Furthermore, we prove an invariance
principle, i.e., a functional limit theorem towards
Dyson's Brownian motions, the continuous analogue.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Doob h-transform; Dyson's Brownian motions;
fluctuation theory.; non-colliding random walks;
non-intersecting random processes; Vandermonde
determinant",
}
@Article{Kulske:2008:PMG,
author = "Christof K{\"u}lske and Alex Opoku",
title = "The posterior metric and the goodness of
{Gibbsianness} for transforms of {Gibbs} measures",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "47:1307--47:1344",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-560",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/560",
abstract = "We present a general method to derive continuity
estimates for conditional probabilities of general
(possibly continuous) spin models subjected to local
transformations. Such systems arise in the study of a
stochastic time-evolution of Gibbs measures or as noisy
observations. Assuming no a priori metric on the local
state spaces but only a measurable structure, we define
the posterior metric on the local image space. We show
that it allows in a natural way to divide the local
part of the continuity estimates from the spatial part
(which is treated by Dobrushin uniqueness here). We
show in the concrete example of the time evolution of
rotators on the $ (q - 1)$-dimensional sphere how this
method can be used to obtain estimates in terms of the
familiar Euclidean metric. In another application we
prove the preservation of Gibbsianness for sufficiently
fine local coarse-grainings when the Hamiltonian
satisfies a Lipschitz property",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "phase transitions; posterior metric; specification;
Time-evolved Gibbs measures, non-Gibbsian measures:
Dobrushin uniqueness",
}
@Article{Collet:2008:RPS,
author = "Pierre Collet and Antonio Galves and Florencia
Leonardi",
title = "Random perturbations of stochastic processes with
unbounded variable length memory",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "48:1345--48:1361",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-538",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/538",
abstract = "We consider binary infinite order stochastic chains
perturbed by a random noise. This means that at each
time step, the value assumed by the chain can be
randomly and independently flipped with a small fixed
probability. We show that the transition probabilities
of the perturbed chain are uniformly close to the
corresponding transition probabilities of the original
chain. As a consequence, in the case of stochastic
chains with unbounded but otherwise finite variable
length memory, we show that it is possible to recover
the context tree of the original chain, using a
suitable version of the algorithm Context, provided
that the noise is small enough.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "chains of infinite order, variable length Markov
chains, chains with unbounded variable length memory,
random perturbations, algorithm Context, context
trees",
}
@Article{Bonaccorsi:2008:SFN,
author = "Stefano Bonaccorsi and Carlo Marinelli and Giacomo
Ziglio",
title = "Stochastic {FitzHugh--Nagumo} equations on networks
with impulsive noise",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "49:1362--49:1379",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-532",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/532",
abstract = "We consider a system of nonlinear partial differential
equations with stochastic dynamical boundary conditions
that arises in models of neurophysiology for the
diffusion of electrical potentials through a finite
network of neurons. Motivated by the discussion in the
biological literature, we impose a general diffusion
equation on each edge through a generalized version of
the FitzHugh--Nagumo model, while the noise acting on
the boundary is described by a generalized stochastic
Kirchhoff law on the nodes. In the abstract framework
of matrix operators theory, we rewrite this stochastic
boundary value problem as a stochastic evolution
equation in infinite dimensions with a power-type
nonlinearity, driven by an additive L{\'e}vy noise. We
prove global well-posedness in the mild sense for such
stochastic partial differential equation by
monotonicity methods.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic PDEs, FitzHugh--Nagumo equation, L{\'e}vy
processes, maximal monotone operators",
}
@Article{Borodin:2008:LTA,
author = "Alexei Borodin and Patrik Ferrari",
title = "Large time asymptotics of growth models on space-like
paths {I}: {PushASEP}",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "50:1380--50:1418",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-541",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/541",
abstract = "We consider a new interacting particle system on the
one-dimensional lattice that interpolates between TASEP
and Toom's model: A particle cannot jump to the right
if the neighboring site is occupied, and when jumping
to the left it simply pushes all the neighbors that
block its way. We prove that for flat and step initial
conditions, the large time fluctuations of the height
function of the associated growth model along any
space-like path are described by the Airy$_1$ and
Airy$_2$ processes. This includes fluctuations of the
height profile for a fixed time and fluctuations of a
tagged particle's trajectory as special cases.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "stochastic growth, KPZ, determinantal processes, Airy
processes",
}
@Article{Croydon:2008:RWG,
author = "David Croydon and Takashi Kumagai",
title = "Random walks on {Galton--Watson} trees with infinite
variance offspring distribution conditioned to
survive",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "51:1419--51:1441",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-536",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/536",
abstract = "We establish a variety of properties of the discrete
time simple random walk on a Galton--Watson tree
conditioned to survive when the offspring distribution,
$Z$ say, is in the domain of attraction of a stable law
with index $ \alpha \in (1, 2]$. In particular, we are
able to prove a quenched version of the result that the
spectral dimension of the random walk is $ 2 \alpha /
(2 \alpha - 1)$. Furthermore, we demonstrate that when
$ \alpha \in (1, 2)$ there are logarithmic fluctuations
in the quenched transition density of the simple random
walk, which contrasts with the log-logarithmic
fluctuations seen when $ \alpha = 2$. In the course of
our arguments, we obtain tail bounds for the
distribution of the $n$ th generation size of a
Galton--Watson branching process with offspring
distribution $Z$ conditioned to survive, as well as
tail bounds for the distribution of the total number of
individuals born up to the $n$ th generation, that are
uniform in $n$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "branching process; random walk; stable distribution;
transition density",
}
@Article{Schweinsberg:2008:WM,
author = "Jason Schweinsberg",
title = "Waiting for $m$ mutations",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "52:1442--52:1478",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-540",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/540",
abstract = "We consider a model of a population of fixed size $N$
in which each individual gets replaced at rate one and
each individual experiences a mutation at rate $ \mu $.
We calculate the asymptotic distribution of the time
that it takes before there is an individual in the
population with $m$ mutations. Several different
behaviors are possible, depending on how ?? changes
with $N$. These results have applications to the
problem of determining the waiting time for regulatory
sequences to appear and to models of cancer
development.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Moran model; mutations; population genetics; Waiting
times",
}
@Article{Voss:2008:LDO,
author = "Jochen Voss",
title = "Large Deviations for One Dimensional Diffusions with a
Strong Drift",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "53:1479--53:1528",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-564",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/564",
abstract = "We derive a large deviation principle which describes
the behaviour of a diffusion process with additive
noise under the influence of a strong drift. Our main
result is a large deviation theorem for the
distribution of the end-point of a one-dimensional
diffusion with drift $ \theta b $ where $b$ is a drift
function and $ \theta $ a real number, when $ \theta $
converges to $ \infty $. It transpires that the problem
is governed by a rate function which consists of two
parts: one contribution comes from the
Freidlin--Wentzell theorem whereas a second term
reflects the cost for a Brownian motion to stay near a
equilibrium point of the drift over long periods of
time.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "diffusion processes; large deviations; stochastic
differential equations",
}
@Article{Confortola:2008:QBR,
author = "Fulvia Confortola and Philippe Briand",
title = "Quadratic {BSDEs} with Random Terminal Time and
Elliptic {PDEs} in Infinite Dimension",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "54:1529--54:1561",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-514",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/514",
abstract = "In this paper we study one dimensional backward
stochastic differential equations (BSDEs) with random
terminal time not necessarily bounded or finite when
the generator $ F(t, Y, Z) $ has a quadratic growth in
$Z$. We provide existence and uniqueness of a bounded
solution of such BSDEs and, in the case of infinite
horizon, regular dependence on parameters. The obtained
results are then applied to prove existence and
uniqueness of a mild solution to elliptic partial
differential equations in Hilbert spaces. Finally we
show an application to a control problem.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "elliptic PDEs; optimal stochastic control; Quadratic
BSDEs",
}
@Article{Nolin:2008:NCP,
author = "Pierre Nolin",
title = "Near-critical percolation in two dimensions",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "55:1562--55:1623",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-565",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/565",
abstract = "We give a self-contained and detailed presentation of
Kesten's results that allow to relate critical and
near-critical percolation on the triangular lattice.
They constitute an important step in the derivation of
the exponents describing the near-critical behavior of
this model. For future use and reference, we also show
how these results can be obtained in more general
situations, and we state some new consequences.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "arm events; critical exponents; near-critical
percolation",
}
@Article{Albenque:2008:SFI,
author = "Marie Albenque and Jean-Fran{\c{c}}ois Marckert",
title = "Some families of increasing planar maps",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "56:1624--56:1671",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-563",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/563",
abstract = "Stack-triangulations appear as natural objects when
one wants to define some families of increasing
triangulations by successive additions of faces. We
investigate the asymptotic behavior of rooted
stack-triangulations with $ 2 n $ faces under two
different distributions. We show that the uniform
distribution on this set of maps converges, for a
topology of local convergence, to a distribution on the
set of infinite maps. In the other hand, we show that
rescaled by $ n^{1 / 2} $, they converge for the
Gromov--Hausdorff topology on metric spaces to the
continuum random tree introduced by Aldous. Under a
distribution induced by a natural random construction,
the distance between random points rescaled by $ (6 /
11) \log n $ converge to 1 in probability. We obtain
similar asymptotic results for a family of increasing
quadrangulations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "stackmaps, triangulations, Gromov--Hausdorff
convergence, continuum random tree",
}
@Article{Kyprianou:2008:SCC,
author = "Andreas Kyprianou and Victor Rivero",
title = "Special, conjugate and complete scale functions for
spectrally negative {L{\'e}vy} processes",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "57:1672--57:1701",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-567",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/567",
abstract = "Following from recent developments in Hubalek and
Kyprianou [28], the objective of this paper is to
provide further methods for constructing new families
of scale functions for spectrally negative L{\'e}vy
processes which are completely explicit. This is the
result of an observation in the aforementioned paper
which permits feeding the theory of Bernstein functions
directly into the Wiener--Hopf factorization for
spectrally negative L{\'e}vy processes. Many new,
concrete examples of scale functions are offered
although the methodology in principle delivers still
more explicit examples than those listed.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Potential theory for subordinators, Scale functions,
Special subordinators, Spectrally negative L{\'e}vy
processes",
}
@Article{Lyons:2008:EUS,
author = "Russell Lyons and Benjamin Morris and Oded Schramm",
title = "Ends in Uniform Spanning Forests",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "58:1702--58:1725",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-566",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/566",
abstract = "It has hitherto been known that in a transitive
unimodular graph, each tree in the wired spanning
forest has only one end a.s. We dispense with the
assumptions of transitivity and unimodularity,
replacing them with a much broader condition on the
isoperimetric profile that requires just slightly more
than uniform transience.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Cayley graphs.; Spanning trees",
}
@Article{Gayrard:2008:EPT,
author = "V{\'e}ronique Gayrard and G{\'e}rard Ben Arous",
title = "Elementary potential theory on the hypercube",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "59:1726--59:1807",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-527",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/527",
abstract = "This work addresses potential theoretic questions for
the standard nearest neighbor random walk on the
hypercube $ \{ - 1, + 1 \}^N $. For a large class of
subsets $ A \subset \{ - 1, + 1 \}^N $ we give precise
estimates for the harmonic measure of $A$, the mean
hitting time of $A$, and the Laplace transform of this
hitting time. In particular, we give precise sufficient
conditions for the harmonic measure to be
asymptotically uniform, and for the hitting time to be
asymptotically exponentially distributed, as $ N
\rightarrow \infty $. Our approach relies on a
$d$-dimensional extension of the Ehrenfest urn scheme
called lumping and covers the case where $d$ is allowed
to diverge with $N$ as long as $ d \leq \alpha_0 \frac
{N}{\log N}$ for some constant $ 0 < \alpha_0 < 1$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "random walk on hypercubes, lumping",
}
@Article{Bass:2008:DSD,
author = "Richard Bass and Edwin Perkins",
title = "Degenerate stochastic differential equations arising
from catalytic branching networks",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "60:1808--60:1885",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-568",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/568",
abstract = "We establish existence and uniqueness for the
martingale problem associated with a system of
degenerate SDE's representing a catalytic branching
network. The drift and branching coefficients are only
assumed to be continuous and satisfy some natural
non-degeneracy conditions. We assume at most one
catalyst per site as is the case for the hypercyclic
equation. Here the two-dimensional case with affine
drift is required in work of [DGHSS] on mean fields
limits of block averages for 2-type branching models on
a hierarchical group. The proofs make use of some new
methods, including Cotlar's lemma to establish
asymptotic orthogonality of the derivatives of an
associated semigroup at different times, and a refined
integration by parts technique from [DP1].",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "catalytic branching; Cotlar's lemma; degenerate
diffusions; martingale problem; perturbations;
resolvents; stochastic differential equations",
}
@Article{Piera:2008:CRR,
author = "Francisco Piera and Ravi Mazumdar",
title = "Comparison Results for Reflected Jump-diffusions in
the Orthant with Variable Reflection Directions and
Stability Applications",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "61:1886--61:1908",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-569",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/569",
abstract = "We consider reflected jump-diffusions in the orthant $
R_+^n $ with time- and state-dependent drift, diffusion
and jump-amplitude coefficients. Directions of
reflection upon hitting boundary faces are also allow
to depend on time and state. Pathwise comparison
results for this class of processes are provided, as
well as absolute continuity properties for their
associated regulator processes responsible of keeping
the respective diffusions in the orthant. An important
role is played by the boundary property in that
regulators do not charge times spent by the reflected
diffusion at the intersection of two or more boundary
faces. The comparison results are then applied to
provide an ergodicity condition for the state-dependent
reflection directions case.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "ergodicity.; Jump-diffusion processes; pathwise
comparisons; Skorokhod maps; stability; state-dependent
oblique reflections",
}
@Article{Veto:2008:SRR,
author = "Balint Veto and Balint Toth",
title = "Self-repelling random walk with directed edges on {$
\mathbb {Z} $}",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "62:1909--62:1926",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-570",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/570",
abstract = "We consider a variant of self-repelling random walk on
the integer lattice Z where the self-repellence is
defined in terms of the local time on oriented edges.
The long-time asymptotic scaling of this walk is
surprisingly different from the asymptotics of the
similar process with self-repellence defined in terms
of local time on unoriented edges. We prove limit
theorems for the local time process and for the
position of the random walker. The main ingredient is a
Ray--Knight-type of approach. At the end of the paper,
we also present some computer simulations which show
the strange scaling behaviour of the walk considered.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "random walks with long memory, self-repelling, one
dimension, oriented edges, local time,
Ray--Knight-theory, coupling",
}
@Article{Amir:2008:SSE,
author = "Gideon Amir and Christopher Hoffman",
title = "A special set of exceptional times for dynamical
random walk on {$ Z^2 $}",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "63:1927--63:1951",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-571",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/571",
abstract = "In [2] Benjamini, H{\"a}ggstr{\"o}m, Peres and Steif
introduced the model of dynamical random walk on the
$d$-dimensional lattice $ Z^d$. This is a continuum of
random walks indexed by a time parameter $t$. They
proved that for dimensions $ d = 3, 4$ there almost
surely exist times $t$ such that the random walk at
time $t$ visits the origin infinitely often, but for
dimension 5 and up there almost surely do not exist
such $t$. Hoffman showed that for dimension 2 there
almost surely exists $t$ such that the random walk at
time $t$ visits the origin only finitely many times
[5]. We refine the results of [5] for dynamical random
walk on $ Z^2$, showing that with probability one the
are times when the origin is visited only a finite
number of times while other points are visited
infinitely often.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Dynamical Random Walks, Dynamical Sensativity; Random
Walks",
}
@Article{Kosygina:2008:PNE,
author = "Elena Kosygina and Martin Zerner",
title = "Positively and negatively excited random walks on
integers, with branching processes",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "64:1952--64:1979",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-572",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/572",
abstract = "We consider excited random walks on the integers with
a bounded number of i.i.d. cookies per site which may
induce drifts both to the left and to the right. We
extend the criteria for recurrence and transience by M.
Zerner and for positivity of speed by A.-L. Basdevant
and A. Singh to this case and also prove an annealed
central limit theorem. The proofs are based on results
from the literature concerning branching processes with
migration and make use of a certain renewal
structure.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Central limit theorem; excited random walk; law of
large numbers; positive and negative cookies;
recurrence; renewal structure; transience",
}
@Article{Bianchi:2008:GDN,
author = "Alessandra Bianchi",
title = "{Glauber} dynamics on nonamenable graphs: boundary
conditions and mixing time",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "65:1980--65:2012",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-574",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/574",
abstract = "We study the stochastic Ising model on finite graphs
with n vertices and bounded degree and analyze the
effect of boundary conditions on the mixing time. We
show that for all low enough temperatures, the spectral
gap of the dynamics with (+)-boundary condition on a
class of nonamenable graphs, is strictly positive
uniformly in n. This implies that the mixing time grows
at most linearly in n. The class of graphs we consider
includes hyperbolic graphs with sufficiently high
degree, where the best upper bound on the mixing time
of the free boundary dynamics is polynomial in n, with
exponent growing with the inverse temperature. In
addition, we construct a graph in this class, for which
the mixing time in the free boundary case is
exponentially large in n. This provides a first example
where the mixing time jumps from exponential to linear
in n while passing from free to (+)-boundary condition.
These results extend the analysis of Martinelli,
Sinclair and Weitz to a wider class of nonamenable
graphs.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Glauber dynamics; mixing time; nonamenable graphs;
spectral gap",
}
@Article{Bordenave:2008:BAP,
author = "Charles Bordenave",
title = "On the birth-and-assassination process, with an
application to scotching a rumor in a network",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "66:2014--66:2030",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-573",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/573",
abstract = "We give new formulas on the total number of born
particles in the stable birth-and-assassination
process, and prove that it has a heavy-tailed
distribution. We also establish that this process is a
scaling limit of a process of rumor scotching in a
network, and is related to a predator-prey dynamics.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "branching process, heavy tail phenomena, SIR
epidemics",
}
@Article{Neuenkirch:2008:DED,
author = "Andreas Neuenkirch and Ivan Nourdin and Samy Tindel",
title = "Delay equations driven by rough paths",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "67:2031--67:2068",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-575",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/575",
abstract = "In this article, we illustrate the flexibility of the
algebraic integration formalism introduced in M.
Gubinelli, {\em J. Funct. Anal.} {\bf 216}, 86-140,
2004,
\url{http://www.ams.org/mathscinet-getitem?mr=2005k:60169}
Math. Review 2005k:60169, by establishing an existence
and uniqueness result for delay equations driven by
rough paths. We then apply our results to the case
where the driving path is a fractional Brownian motion
with Hurst parameter $ H > 1 / 3 $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "delay equation; fractional Brownian motion; Malliavin
calculus; rough paths theory",
}
@Article{Hermisson:2008:PGH,
author = "Joachim Hermisson and Peter Pfaffelhuber",
title = "The pattern of genetic hitchhiking under recurrent
mutation",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "68:2069--68:2106",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-577",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/577",
abstract = "Genetic hitchhiking describes evolution at a neutral
locus that is linked to a selected locus. If a
beneficial allele rises to fixation at the selected
locus, a characteristic polymorphism pattern (so-called
selective sweep) emerges at the neutral locus. The
classical model assumes that fixation of the beneficial
allele occurs from a single copy of this allele that
arises by mutation. However, recent theory (Pennings
and Hermisson, 2006a, b) has shown that recurrent
beneficial mutation at biologically realistic rates can
lead to markedly different polymorphism patterns,
so-called soft selective sweeps. We extend an approach
that has recently been developed for the classical
hitchhiking model (Schweinsberg and Durrett, 2005;
Etheridge et al., 2006) to study the recurrent mutation
scenario. We show that the genealogy at the neutral
locus can be approximated (to leading orders in the
selection strength) by a marked Yule process with
immigration. Using this formalism, we derive an
improved analytical approximation for the expected
heterozygosity at the neutral locus at the time of
fixation of the beneficial allele.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Selective sweep, genetic hitchhiking, soft selective
sweep, diffusion approximation, Yule process, random
background",
}
@Article{Arguin:2008:CPS,
author = "Louis-Pierre Arguin",
title = "Competing Particle Systems and the {Ghirlanda--Guerra}
Identities",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "69:2101--69:2117",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-579",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/579",
abstract = "Competing particle systems are point processes on the
real line whose configurations $X$ can be ordered
decreasingly and evolve by increments which are
functions of correlated Gaussian variables. The
correlations are intrinsic to the points and quantified
by a matrix $ Q = \{ q_{ij} \} $. Quasi-stationary
systems are those for which the law of $ (X, Q)$ is
invariant under the evolution up to translation of $X$.
It was conjectured by Aizenman and co-authors that the
matrix $Q$ of robustly quasi-stationary systems must
exhibit a hierarchical structure. This was established
recently, up to a natural decomposition of the system,
whenever the set $ S_Q$ of values assumed by $ q_{ij}$
is finite. In this paper, we study the general case
where $ S_Q$ may be infinite. Using the past increments
of the evolution, we show that the law of robustly
quasi-stationary systems must obey the
Ghirlanda--Guerra identities, which first appear in the
study of spin glass models. This provides strong
evidence that the above conjecture also holds in the
general case. In addition, it yields an alternative
proof of a theorem of Ruzmaikina and Aizenman for
independent increments.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Point processes, Ultrametricity, Ghirlanda--Guerra
identities",
}
@Article{Garet:2008:FPC,
author = "Olivier Garet and R{\'e}gine Marchand",
title = "First-passage competition with different speeds:
positive density for both species is impossible",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "70:2118--70:2159",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-581",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/581",
abstract = "Consider two epidemics whose expansions on $ \mathbb
{Z}^d $ are governed by two families of passage times
that are distinct and stochastically comparable. We
prove that when the weak infection survives, the space
occupied by the strong one is almost impossible to
detect. Particularly, in dimension two, we prove that
one species finally occupies a set with full density,
while the other one only occupies a set of null
density. Furthermore, we observe the same fluctuations
with respect to the asymptotic shape as for the weak
infection evolving alone. By the way, we extend the
H{\"a}ggstr{\"o}m-Pemantle non-coexistence result
``except perhaps for a denumerable set'' to families of
stochastically comparable passage times indexed by a
continuous parameter.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "coexistence; competition; first-passage percolation;
moderate deviations; random growth",
}
@Article{Athreya:2008:RDT,
author = "Siva Athreya and Rahul Roy and Anish Sarkar",
title = "Random directed trees and forest --- drainage networks
with dependence",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "71:2160--71:2189",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-580",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/580",
abstract = "Consider the $d$-dimensional lattice $ \mathbb Z^d$
where each vertex is `open' or `closed' with
probability $p$ or $ 1 - p$ respectively. An open
vertex $v$ is connected by an edge to the closest open
vertex $ w$ in the $ 45^\circ $ (downward) light cone
generated at $v$. In case of non-uniqueness of such a
vertex $w$, we choose any one of the closest vertices
with equal probability and independently of the other
random mechanisms. It is shown that this random graph
is a tree almost surely for $ d = 2$ and $3$ and it is
an infinite collection of distinct trees for $ d \geq
4$. In addition, for any dimension, we show that there
is no bi-infinite path in the tree.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Random Graph, Random Oriented Trees, Random Walk",
}
@Article{Heunis:2008:ICN,
author = "Andrew Heunis and Vladimir Lucic",
title = "On the Innovations Conjecture of Nonlinear Filtering
with Dependent Data",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "72:2190--72:2216",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-585",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/585",
abstract = "We establish the innovations conjecture for a
nonlinear filtering problem in which the signal to be
estimated is conditioned by the observations. The
approach uses only elementary stochastic analysis,
together with a variant due to J. M. C. Clark of a
theorem of Yamada and Watanabe on pathwise-uniqueness
and strong solutions of stochastic differential
equations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "innovations conjecture; nonlinear filter;
pathwise-uniqueness",
}
@Article{Faggionato:2008:RWE,
author = "Alessandra Faggionato",
title = "Random walks and exclusion processes among random
conductances on random infinite clusters:
homogenization and hydrodynamic limit",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "73:2217--73:2247",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-591",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/591",
abstract = "We consider a stationary and ergodic random field $ \{
\omega (b) \colon b \in \mathbb {E}_d \} $
parameterized by the family of bonds in $ \mathbb {Z}^d
$, $ d \geq 2 $. The random variable $ \omega (b) $ is
thought of as the conductance of bond $b$ and it ranges
in a finite interval $ [0, c_0]$. Assuming that the set
of bonds with positive conductance has a unique
infinite cluster $ \mathcal {C}(\omega)$, we prove
homogenization results for the random walk among random
conductances on $ \mathcal {C}(\omega)$. As a
byproduct, applying the general criterion of Faggionato
(2007) leading to the hydrodynamic limit of exclusion
processes with bond--dependent transition rates, for
almost all realizations of the environment we prove the
hydrodynamic limit of simple exclusion processes among
random conductances on $ \mathcal {C}(\omega)$. The
hydrodynamic equation is given by a heat equation whose
diffusion matrix does not depend on the environment. We
do not require any ellipticity condition. As special
case, $ \mathcal {C}(\omega)$ can be the infinite
cluster of supercritical Bernoulli bond percolation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "bond percolation; disordered system; exclusion
process; homogenization; random walk in random
environment",
}
@Article{Mueller:2008:RDS,
author = "Carl Mueller and David Nualart",
title = "Regularity of the density for the stochastic heat
equation",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "74:2248--74:2258",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-589",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/589",
abstract = "We study the smoothness of the density of a semilinear
heat equation with multiplicative spacetime white
noise. Using Malliavin calculus, we reduce the problem
to a question of negative moments of solutions of a
linear heat equation with multiplicative white noise.
Then we settle this question by proving that solutions
to the linear equation have negative moments of all
orders.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "heat equation, white noise, Malliavin calculus,
stochastic partial differential equations",
}
@Article{Zemlys:2008:HFS,
author = "Vaidotas Zemlys",
title = "A {H{\"o}lderian} {FCLT} for some multiparameter
summation process of independent non-identically
distributed random variables",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "75:2259--75:2282",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-590",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/590",
abstract = "We introduce a new construction of a summation process
based on the collection of rectangular subsets of unit
d-dimensional cube for a triangular array of
independent non-identically distributed variables with
d-dimensional index, using the non-uniform grid adapted
to the variances of the variables. We investigate its
convergence in distribution in some Holder spaces. It
turns out that for dimensions greater than 2, the
limiting process is not necessarily the standard
Brownian sheet. This contrasts with a classical result
of Prokhorov for the one-dimensional case.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian sheet, functional central limit theorem,
H{\"o}lder space, invariance principle, triangular
array, summation process.",
}
@Article{Drewitz:2008:LEO,
author = "Alexander Drewitz",
title = "{Lyapunov} exponents for the one-dimensional parabolic
{Anderson} model with drift",
journal = j-ELECTRON-J-PROBAB,
volume = "13",
pages = "76:2283--76:2336",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v13-586",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/586",
abstract = "We consider the solution to the one-dimensional
parabolic Anderson model with homogeneous initial
condition, arbitrary drift and a time-independent
potential bounded from above. Under ergodicity and
independence conditions we derive representations for
both the quenched Lyapunov exponent and, more
importantly, the $p$-th annealed Lyapunov exponents for
all positive real $p$. These results enable us to prove
the heuristically plausible fact that the $p$-th
annealed Lyapunov exponent converges to the quenched
Lyapunov exponent as $p$ tends to 0. Furthermore, we
show that the solution is $p$-intermittent for $p$
large enough. As a byproduct, we compute the optimal
quenched speed of the random walk appearing in the
Feynman--Kac representation of the solution under the
corresponding Gibbs measure. In our context, depending
on the negativity of the potential, a phase transition
from zero speed to positive speed appears as the drift
parameter or diffusion constant increase,
respectively.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Parabolic Anderson model, Lyapunov exponents,
intermittency, large deviations",
}
@Article{Hambly:2009:PHI,
author = "Ben Hambly and Martin Barlow",
title = "Parabolic {Harnack} inequality and local limit theorem
for percolation clusters",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "1:1--1:26",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-587",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/587",
abstract = "We consider the random walk on supercritical
percolation clusters in $ \mathbb {Z}^d $. Previous
papers have obtained Gaussian heat kernel bounds, and
a.s. invariance principles for this process. We show
how this information leads to a parabolic Harnack
inequality, a local limit theorem and estimates on the
Green's function.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Harnack inequality; local limit theorem; Percolation;
random walk",
}
@Article{Douc:2009:FIC,
author = "Randal Douc and Eric Moulines and Yaacov Ritov",
title = "Forgetting of the initial condition for the filter in
general state-space hidden {Markov} chain: a coupling
approach",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "2:27--2:49",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-593",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/593",
abstract = "We give simple conditions that ensure exponential
forgetting of the initial conditions of the filter for
general state-space hidden Markov chain. The proofs are
based on the coupling argument applied to the posterior
Markov kernels. These results are useful both for
filtering hidden Markov models using approximation
methods (e.g., particle filters) and for proving
asymptotic properties of estimators. The results are
general enough to cover models like the Gaussian state
space model, without using the special structure that
permits the application of the Kalman filter.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "hidden Markov chain; non-linear filtering, coupling;
stability",
}
@Article{Atar:2009:ETG,
author = "Rami Atar and Siva Athreya and Zhen-Qing Chen",
title = "Exit Time, Green Function and Semilinear Elliptic
Equations",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "3:50--3:71",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-597",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/597",
abstract = "Let $D$ be a bounded Lipschitz domain in $ R^n$ with $
n \geq 2$ and $ \tau_D$ be the first exit time from $D$
by Brownian motion on $ R^n$. In the first part of this
paper, we are concerned with sharp estimates on the
expected exit time $ E_x [\tau_D]$. We show that if $D$
satisfies a uniform interior cone condition with angle
$ \theta \in (\cos^{-1}(1 / \sqrt {n}), \pi)$, then $
c_1 \varphi_1 (x) \leq E_x [\tau_D] \leq c_2 \varphi_1
(x)$ on $D$. Here $ \varphi_1$ is the first positive
eigenfunction for the Dirichlet Laplacian on $D$. The
above result is sharp as we show that if $D$ is a
truncated circular cone with angle $ \theta <
\cos^{-1}(1 / \sqrt {n})$, then the upper bound for $
E_x [\tau_D]$ fails. These results are then used in the
second part of this paper to investigate whether
positive solutions of the semilinear equation $ \Delta
u = u^p$ in $ D, $ $ p \in R$, that vanish on an open
subset $ \Gamma \subset \partial D$ decay at the same
rate as $ \varphi_1$ on $ \Gamma $.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "boundary Harnack principle; Brownian motion; Dirichlet
Laplacian; exit time; Feynman--Kac transform; Green
function estimates; ground state; Lipschitz domain;
Schauder's fixed point theorem; semilinear elliptic
equation",
}
@Article{Ibarrola:2009:FTR,
author = "Ricardo V{\'e}lez Ibarrola and Tomas Prieto-Rumeau",
title = "{De Finetti}'s-type results for some families of non
identically distributed random variables",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "4:72--4:86",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-602",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/602",
abstract = "We consider random selection processes of weighted
elements in an arbitrary set. Their conditional
distributions are shown to be a generalization of the
hypergeometric distribution, while the marginal
distributions can always be chosen as generalized
binomial distributions. Then we propose sufficient
conditions on the weight function ensuring that the
marginal distributions are necessarily of the
generalized binomial form. In these cases, the
corresponding indicator random variables are
conditionally independent (as in the classical De
Finetti theorem) though they are neither exchangeable
nor identically distributed.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "De Finetti theorem; exchangeability; random assignment
processes",
}
@Article{Janson:2009:PRG,
author = "Svante Janson",
title = "On percolation in random graphs with given vertex
degrees",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "5:86--5:118",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-603",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/603",
abstract = "We study the random graph obtained by random deletion
of vertices or edges from a random graph with given
vertex degrees. A simple trick of exploding vertices
instead of deleting them, enables us to derive results
from known results for random graphs with given vertex
degrees. This is used to study existence of giant
component and existence of k-core. As a variation of
the latter, we study also bootstrap percolation in
random regular graphs. We obtain both simple new proofs
of known results and new results. An interesting
feature is that for some degree sequences, there are
several or even infinitely many phase transitions for
the k-core.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "bootstrap percolation; giant component; k-core; random
graph",
}
@Article{Sega:2009:LRC,
author = "Gregor Sega",
title = "Large-range constant threshold growth model in one
dimension",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "6:119--6:138",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-598",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/598",
abstract = "We study a one dimensional constant threshold model in
continuous time. Its dynamics have two parameters, the
range $n$ and the threshold $v$. An unoccupied site $x$
becomes occupied at rate 1 as soon as there are at
least $v$ occupied sites in $ [x - n, x + n]$. As n
goes to infinity and $v$ is kept fixed, the dynamics
can be approximated by a continuous space version,
which has an explicit invariant measure at the front.
This allows us to prove that the speed of propagation
is asymptoticaly $ n^2 / 2 v$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "asymptotic propagation velocity; growth model;
invariant distribution",
}
@Article{Weiss:2009:EBS,
author = "Alexander Weiss",
title = "Escaping the {Brownian} stalkers",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "7:139--7:160",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-594",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/594",
abstract = "We propose a simple model for the behaviour of
longterm investors on a stock market. It consists of
three particles that represent the stock's current
price and the buyers', respectively sellers', opinion
about the right trading price. As time evolves, both
groups of traders update their opinions with respect to
the current price. The speed of updating is controlled
by a parameter; the price process is described by a
geometric Brownian motion. We consider the market's
stability in terms of the distance between the buyers'
and sellers' opinion, and prove that the distance
process is recurrent/transient in dependence on the
parameter.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "financial markets; market stability; recurrence;
stochastic dynamics; transience",
}
@Article{Bovier:2009:ASS,
author = "Anton Bovier and Anton Klimovsky",
title = "The {Aizenman--Sims--Starr} and {Guerras} schemes for
the {SK} model with multidimensional spins",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "8:161--8:241",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-611",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/611",
abstract = "We prove upper and lower bounds on the free energy of
the Sherrington--Kirkpatrick model with
multidimensional spins in terms of variational
inequalities. The bounds are based on a
multidimensional extension of the Parisi functional. We
generalise and unify the comparison scheme of Aizenman,
Sims and Starr and the one of Guerra involving the
GREM-inspired processes and Ruelle's probability
cascades. For this purpose, an abstract quenched large
deviations principle of the G{\"a}rtner-Ellis type is
obtained. We derive Talagrand's representation of
Guerra's remainder term for the
Sherrington--Kirkpatrick model with multidimensional
spins. The derivation is based on well-known properties
of Ruelle's probability cascades and the
Bolthausen--Sznitman coalescent. We study the
properties of the multidimensional Parisi functional by
establishing a link with a certain class of semi-linear
partial differential equations. We embed the problem of
strict convexity of the Parisi functional in a more
general setting and prove the convexity in some
particular cases which shed some light on the original
convexity problem of Talagrand. Finally, we prove the
Parisi formula for the local free energy in the case of
multidimensional Gaussian a priori distribution of
spins using Talagrand's methodology of a priori
estimates.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Sherrington--Kirkpatrick model, multidimensional
spins, quenched large deviations, concentration of
measure, Gaussian spins, convexity, Parisi functional,
Parisi formula",
}
@Article{Taylor:2009:CPS,
author = "Jesse Taylor and Amandine V{\'e}ber",
title = "Coalescent processes in subdivided populations subject
to recurrent mass extinctions",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "9:242--9:288",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-595",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/595",
abstract = "We investigate the infinitely many demes limit of the
genealogy of a sample of individuals from a subdivided
population that experiences sporadic mass extinction
events. By exploiting a separation of time scales that
occurs within a class of structured population models
generalizing Wright's island model, we show that as the
number of demes tends to infinity, the limiting form of
the genealogy can be described in terms of the
alternation of instantaneous scattering phases that
depend mainly on local demographic processes, and
extended collecting phases that are dominated by global
processes. When extinction and recolonization events
are local, the genealogy is described by Kingman's
coalescent, and the scattering phase influences only
the overall rate of the process. In contrast, if the
demes left vacant by a mass extinction event are
recolonized by individuals emerging from a small number
of demes, then the limiting genealogy is a coalescent
process with simultaneous multiple mergers (a $ \Xi
$-coalescent). In this case, the details of the
within-deme population dynamics influence not only the
overall rate of the coalescent process, but also the
statistics of the complex mergers that can occur within
sample genealogies. These results suggest that the
combined effects of geography and disturbance could
play an important role in producing the unusual
patterns of genetic variation documented in some marine
organisms with high fecundity.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "disturbance; extinction/recolonization; genealogy;
metapopulation; population genetics; separation of time
scales; Xi-coalescent",
}
@Article{Alsmeyer:2009:LTM,
author = "Gerold Alsmeyer and Alex Iksanov",
title = "A Log-Type Moment Result for Perpetuities and Its
Application to Martingales in Supercritical Branching
Random Walks",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "10:289--10:313",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-596",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/596",
abstract = "Infinite sums of i.i.d. random variables discounted by
a multiplicative random walk are called perpetuities
and have been studied by many authors. The present
paper provides a log-type moment result for such random
variables under minimal conditions which is then
utilized for the study of related moments of a.s.
limits of certain martingales associated with the
supercritical branching random walk. The connection
arises upon consideration of a size-biased version of
the branching random walk originally introduced by
Lyons. As a by-product, necessary and sufficient
conditions for uniform integrability of these
martingales are provided in the most general situation
which particularly means that the classical
(LlogL)-condition is not always needed.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "branching random walk; martingale; moments;
perpetuity",
}
@Article{Foondun:2009:HKE,
author = "Mohammud Foondun",
title = "Heat kernel estimates and {Harnack} inequalities for
some {Dirichlet} forms with non-local part",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "11:314--11:340",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-604",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/604",
abstract = "We consider the Dirichlet form given by\par
$$ {\cal E}(f, f) = \frac {1}{2} \int_{R^d} \sum_{i, j
= 1}^d a_{ij}(x) \frac {\partial f(x)}{\partial x_i}
\frac {\partial f(x)}{\partial x_j} d x $$
$$ + \int_{R^d \times R^d} (f(y) - f(x))^2 J(x, y)d x
d y. $$
Under the assumption that the $ {a_{ij}} $ are
symmetric and uniformly elliptic and with suitable
conditions on $J$, the nonlocal part, we obtain upper
and lower bounds on the heat kernel of the Dirichlet
form. We also prove a Harnack inequality and a
regularity theorem for functions that are harmonic with
respect to $ \cal E$.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Integro-differential operators. Harnack inequality.
Heat kernel, Holder continuity",
}
@Article{Lejay:2009:RDE,
author = "Antoine Lejay",
title = "On rough differential equations",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "12:341--12:364",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-613",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/613",
abstract = "We prove that the It{\^o} map, that is the map that
gives the solution of a differential equation
controlled by a rough path of finite $p$-variation with
$ p \in [2, 3)$ is locally Lipschitz continuous in all
its arguments and we give some sufficient conditions
for global existence for non-bounded vector fields.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
}
@Article{Barbour:2009:SCI,
author = "A. Barbour and A. Gnedin",
title = "Small counts in the infinite occupancy scheme",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "13:365--13:384",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-608",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/608",
abstract = "The paper is concerned with the classical occupancy
scheme in which balls are thrown independently into
infinitely many boxes, with given probability of
hitting each of the boxes. We establish joint normal
approximation, as the number of balls goes to infinity,
for the numbers of boxes containing any fixed number of
balls, standardized in the natural way, assuming only
that the variances of these counts all tend to
infinity. The proof of this approximation is based on a
de-Poissonization lemma. We then review sufficient
conditions for the variances to tend to infinity.
Typically, the normal approximation does not mean
convergence. We show that the convergence of the full
vector of counts only holds under a condition of
regular variation, thus giving a complete
characterization of possible limit correlation
structures.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "normal approximation; occupancy problem;
Poissonization; regular variation",
}
@Article{Gravner:2009:LBP,
author = "Janko Gravner and Alexander Holroyd",
title = "Local Bootstrap Percolation",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "14:385--14:399",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-607",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/607",
abstract = "We study a variant of bootstrap percolation in which
growth is restricted to a single active cluster.
Initially there is a single {\em active} site at the
origin, while other sites of $ \mathbb {Z}^2 $ are
independently {\em occupied} with small probability
$p$, otherwise {\em empty}. Subsequently, an empty site
becomes active by contact with two or more active
neighbors, and an occupied site becomes active if it
has an active site within distance 2. We prove that the
entire lattice becomes active with probability $ \exp
[\alpha (p) / p]$, where $ \alpha (p)$ is between $ -
\pi^2 / 9 + c \sqrt p$ and $ - \pi^2 / 9 + C \sqrt
p(\log p^{-1})^3$. This corrects previous numerical
predictions for the scaling of the correction term.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "bootstrap percolation; cellular automaton; crossover;
finite-size scaling; metastability",
}
@Article{Chen:2009:NFM,
author = "Bo Chen and Daniel Ford and Matthias Winkel",
title = "A new family of {Markov} branching trees: the
alpha-gamma model",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "15:400--15:430",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-616",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/616",
abstract = "We introduce a simple tree growth process that gives
rise to a new two-parameter family of discrete
fragmentation trees that extends Ford's alpha model to
multifurcating trees and includes the trees obtained by
uniform sampling from Duquesne and Le Gall's stable
continuum random tree. We call these new trees the
alpha-gamma trees. In this paper, we obtain their
splitting rules, dislocation measures both in ranked
order and in size-biased order, and we study their
limiting behaviour.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Alpha-gamma tree, splitting rule, sampling
consistency, self-similar fragmentation, dislocation
measure, continuum random tree, R-tree, Markov
branching model",
}
@Article{Tournier:2009:IET,
author = "Laurent Tournier",
title = "Integrability of exit times and ballisticity for
random walks in {Dirichlet} environment",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "16:431--16:451",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-609",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/609",
abstract = "We consider random walks in Dirichlet random
environment. Since the Dirichlet distribution is not
uniformly elliptic, the annealed integrability of the
exit time out of a given finite subset is a non-trivial
question. In this paper we provide a simple and
explicit equivalent condition for the integrability of
Green functions and exit times on any finite directed
graph. The proof relies on a quotienting procedure
allowing for an induction argument on the cardinality
of the graph. This integrability problem arises in the
definition of Kalikow auxiliary random walk. Using a
particular case of our condition, we prove a refined
version of the ballisticity criterion given by Enriquez
and Sabot.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "ballisticity; Dirichlet distribution; exit time;
quotient graph; random walks in random environment;
reinforced random walks",
}
@Article{Bryc:2009:DRQ,
author = "W{\l}odek Bryc and Virgil Pierce",
title = "Duality of real and quaternionic random matrices",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "17:452--17:476",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-606",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/606",
abstract = "We show that quaternionic Gaussian random variables
satisfy a generalization of the Wick formula for
computing the expected value of products in terms of a
family of graphical enumeration problems. When applied
to the quaternionic Wigner and Wishart families of
random matrices the result gives the duality between
moments of these families and the corresponding real
Wigner and Wishart families.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Gaussian Symplectic Ensemble, quaternion Wishart,
moments, Mobius graphs, Euler characteristic",
}
@Article{Bahlali:2009:HSP,
author = "Khaled Bahlali and A. Elouaflin and Etienne Pardoux",
title = "Homogenization of semilinear {PDEs} with discontinuous
averaged coefficients",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "18:477--18:499",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-627",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/627",
abstract = "We study the asymptotic behavior of solutions of
semilinear PDEs. Neither periodicity nor ergodicity
will be assumed. On the other hand, we assume that the
coefficients have averages in the Cesaro sense. In such
a case, the averaged coefficients could be
discontinuous. We use a probabilistic approach based on
weak convergence of the associated backward stochastic
dierential equation (BSDE) in the Jakubowski
$S$-topology to derive the averaged PDE. However, since
the averaged coefficients are discontinuous, the
classical viscosity solution is not defined for the
averaged PDE. We then use the notion of ``$
L_p$-viscosity solution'' introduced in [7]. The
existence of $ L_p$-viscosity solution to the averaged
PDE is proved here by using BSDEs techniques.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Backward stochastic differential equations (BSDEs),
$L^p$-viscosity solution for PDEs, homogenization,
Jakubowski S-topology, limit in the Cesaro sense",
}
@Article{Denis:2009:MPC,
author = "Laurent Denis and Anis Matoussi and Lucretiu Stoica",
title = "Maximum Principle and Comparison Theorem for
Quasi-linear Stochastic {PDE}'s",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "19:500--19:530",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-629",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/629",
abstract = "We prove a comparison theorem and maximum principle
for a local solution of quasi-linear parabolic
stochastic PDEs, similar to the well known results in
the deterministic case. The proofs are based on a
version of It{\^o}'s formula and estimates for the
positive part of a local solution which is non-positive
on the lateral boundary. Moreover we shortly indicate
how these results generalize for Burgers type SPDEs",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic partial differential equation, It{\^o}'s
formula, Maximum principle, Moser's iteration",
}
@Article{Toninelli:2009:CGF,
author = "Fabio Toninelli",
title = "Coarse graining, fractional moments and the critical
slope of random copolymers",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "20:531--20:547",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-612",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/612",
abstract = "For a much-studied model of random copolymer at a
selective interface we prove that the slope of the
critical curve in the weak-disorder limit is strictly
smaller than 1, which is the value given by the
annealed inequality. The proof is based on a
coarse-graining procedure, combined with upper bounds
on the fractional moments of the partition function.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Coarse-graining; Copolymers at Selective Interfaces;
Fractional Moment Estimates",
}
@Article{Foondun:2009:INP,
author = "Mohammud Foondun and Davar Khoshnevisan",
title = "Intermittence and nonlinear parabolic stochastic
partial differential equations",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "21:548--21:568",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-614",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/614",
abstract = "We consider nonlinear parabolic SPDEs of the form $
\partial_t u = {\cal L} u + \sigma (u) \dot w $, where
$ \dot w $ denotes space-time white noise, $ \sigma
\colon R \to R $ is [globally] Lipschitz continuous,
and $ \cal L $ is the $ L^2$-generator of a L'evy
process. We present precise criteria for existence as
well as uniqueness of solutions. More significantly, we
prove that these solutions grow in time with at most a
precise exponential rate. We establish also that when $
\sigma $ is globally Lipschitz and asymptotically
sublinear, the solution to the nonlinear heat equation
is ``weakly intermittent, '' provided that the
symmetrization of $ \cal L$ is recurrent and the
initial data is sufficiently large. Among other things,
our results lead to general formulas for the upper
second-moment Liapounov exponent of the parabolic
Anderson model for $ \cal L$ in dimension $ (1 + 1)$.
When $ {\cal L} = \kappa \partial_{xx}$ for $ \kappa >
0$, these formulas agree with the earlier results of
statistical physics (Kardar (1987), Krug and Spohn
(1991), Lieb and Liniger (1963)), and also probability
theory (Bertini and Cancrini (1995), Carmona and
Molchanov (1994)) in the two exactly-solvable cases.
That is when $ u_0 = \delta_0$ or $ u_0 \equiv 1$; in
those cases the moments of the solution to the SPDE can
be computed (Bertini and Cancrini (1995)).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Stochastic partial differential equations, Levy
processes",
}
@Article{Gantert:2009:STR,
author = "Nina Gantert and Serguei Popov and Marina
Vachkovskaia",
title = "Survival time of random walk in random environment
among soft obstacles",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "22:569--22:593",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-631",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/631",
abstract = "We consider a Random Walk in Random Environment (RWRE)
moving in an i.i.d. random field of obstacles. When the
particle hits an obstacle, it disappears with a
positive probability. We obtain quenched and annealed
bounds on the tails of the survival time in the general
$d$-dimensional case. We then consider a simplified
one-dimensional model (where transition probabilities
and obstacles are independent and the RWRE only moves
to neighbour sites), and obtain finer results for the
tail of the survival time. In addition, we study also
the ``mixed'' probability measures (quenched with
respect to the obstacles and annealed with respect to
the transition probabilities and vice-versa) and give
results for tails of the survival time with respect to
these probability measures. Further, we apply the same
methods to obtain bounds for the tails of hitting times
of Branching Random Walks in Random Environment
(BRWRE).",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "confinement of RWRE, survival time, quenched and
annealed tails, nestling RWRE, branching random walks
in random environment",
}
@Article{Matsui:2009:EFO,
author = "Muneya Matsui and Narn-Rueih Shieh",
title = "On the Exponentials of Fractional
{Ornstein--Uhlenbeck} Processes",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "23:594--23:611",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-628",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/628",
abstract = "We study the correlation decay and the expected
maximal increment (Burkholder--Davis--Gundy type
inequalities) of the exponential process determined by
a fractional Ornstein--Uhlenbeck process. The method is
to apply integration by parts formula on integral
representations of fractional Ornstein--Uhlenbeck
processes, and also to use Slepian's inequality. As an
application, we attempt Kahane's T-martingale theory
based on our exponential process which is shown to be
of long memory.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Long memory (Long range dependence), Fractional
Brownian motion, Fractional Ornstein--Uhlenbeck
process, Exponential process, Burkholder--Davis--Gundy
inequalities",
}
@Article{Chassagneux:2009:RCL,
author = "Jean-Fran{\c{c}}ois Chassagneux and Bruno Bouchard",
title = "Representation of continuous linear forms on the set
of ladlag processes and the hedging of {American}
claims under proportional costs",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "24:612--24:632",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-625",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/625",
abstract = "We discuss a d-dimensional version (for l{\`a}dl{\`a}g
optional processes) of a duality result by Meyer (1976)
between {bounded} c{\`a}dl{\`a}g adapted processes and
random measures. We show that it allows to establish,
in a very natural way, a dual representation for the
set of initial endowments which allow to super-hedge a
given American claim in a continuous time model with
proportional transaction costs. It generalizes a
previous result of Bouchard and Temam (2005) who
considered a discrete time setting. It also completes
the very recent work of Denis, De Valli{\`e}re and
Kabanov (2008) who studied c{\`a}dl{\`a}g American
claims and used a completely different approach.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "American options; Randomized stopping times;
transaction costs",
}
@Article{Kuwada:2009:CMM,
author = "Kazumasa Kuwada",
title = "Characterization of maximal {Markovian} couplings for
diffusion processes",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "25:633--25:662",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-634",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/634",
abstract = "Necessary conditions for the existence of a maximal
Markovian coupling of diffusion processes are studied.
A sufficient condition described as a global symmetry
of the processes is revealed to be necessary for the
Brownian motion on a Riemannian homogeneous space. As a
result, we find many examples of a diffusion process
which admits no maximal Markovian coupling. As an
application, we find a Markov chain which admits no
maximal Markovian coupling for specified starting
points.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Maximal coupling, Markovian coupling, diffusion
process, Markov chain",
}
@Article{Pinelis:2009:OTV,
author = "Iosif Pinelis",
title = "Optimal two-value zero-mean disintegration of
zero-mean random variables",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "26:663--26:727",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-633",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/633",
abstract = "For any continuous zero-mean random variable $X$, a
reciprocating function $r$ is constructed, based only
on the distribution of $X$, such that the conditional
distribution of $X$ given the (at-most-)two-point set $
\{ X, r(X) \} $ is the zero-mean distribution on this
set; in fact, a more general construction without the
continuity assumption is given in this paper, as well
as a large variety of other related results, including
characterizations of the reciprocating function and
modeling distribution asymmetry patterns. The mentioned
disintegration of zero-mean r.v.'s implies, in
particular, that an arbitrary zero-mean distribution is
represented as the mixture of two-point zero-mean
distributions; moreover, this mixture representation is
most symmetric in a variety of senses. Somewhat similar
representations - of any probability distribution as
the mixture of two-point distributions with the same
skewness coefficient (but possibly with different
means) - go back to Kolmogorov; very recently, Aizenman
et al. further developed such representations and
applied them to (anti-)concentration inequalities for
functions of independent random variables and to
spectral localization for random Schroedinger
operators. One kind of application given in the present
paper is to construct certain statistical tests for
asymmetry patterns and for location without symmetry
conditions. Exact inequalities implying conservative
properties of such tests are presented. These
developments extend results established earlier by
Efron, Eaton, and Pinelis under a symmetry condition.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Disintegration of measures, Wasserstein metric,
Kantorovich-Rubinstein theorem, transportation of
measures, optimal matching, most symmetric, hypothesis
testing, confidence regions, Student's t-test,
asymmetry, exact inequalities, conservative
properties",
}
@Article{Shkolnikov:2009:CPS,
author = "Mykhaylo Shkolnikov",
title = "Competing Particle Systems Evolving by {I.I.D.}
Increments",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "27:728--27:751",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-635",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/635",
abstract = "We consider competing particle systems in $ \mathbb
{R}^d $, i.e., random locally finite upper bounded
configurations of points in $ \mathbb {R}^d $ evolving
in discrete time steps. In each step i.i.d. increments
are added to the particles independently of the initial
configuration and the previous steps. Ruzmaikina and
Aizenman characterized quasi-stationary measures of
such an evolution, i.e., point processes for which the
joint distribution of the gaps between the particles is
invariant under the evolution, in case $ d = 1 $ and
restricting to increments having a density and an
everywhere finite moment generating function. We prove
corresponding versions of their theorem in dimension $
d = 1 $ for heavy-tailed increments in the domain of
attraction of a stable law and in dimension $ d \geq 1
$ for lattice type increments with an everywhere finite
moment generating function. In all cases we only assume
that under the initial configuration no two particles
are located at the same point. In addition, we analyze
the attractivity of quasi-stationary Poisson point
processes in the space of all Poisson point processes
with almost surely infinite, locally finite and upper
bounded configurations.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Competing particle systems, Large deviations, Spin
glasses",
}
@Article{Delyon:2009:EIS,
author = "Bernard Delyon",
title = "Exponential inequalities for sums of weakly dependent
variables",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "28:752--28:779",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-636",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/636",
abstract = "We give new exponential inequalities and Gaussian
approximation results for sums of weakly dependent
variables. These results lead to generalizations of
Bernstein and Hoeffding inequalities, where an extra
control term is added; this term contains conditional
moments of the variables.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Mixing, exponential inequality; random fields; weak
dependence",
}
@Article{Woodard:2009:SCT,
author = "Dawn Woodard and Scott Schmidler and Mark Huber",
title = "Sufficient Conditions for Torpid Mixing of Parallel
and Simulated Tempering",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "29:780--29:804",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-638",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/638",
abstract = "We obtain upper bounds on the spectral gap of Markov
chains constructed by parallel and simulated tempering,
and provide a set of sufficient conditions for torpid
mixing of both techniques. Combined with the results of
Woodard, Schmidler and Huber (2009), these results
yield a two-sided bound on the spectral gap of these
algorithms. We identify a persistence property of the
target distribution, and show that it can lead
unexpectedly to slow mixing that commonly used
convergence diagnostics will fail to detect. For a
multimodal distribution, the persistence is a measure
of how ``spiky'', or tall and narrow, one peak is
relative to the other peaks of the distribution. We
show that this persistence phenomenon can be used to
explain the torpid mixing of parallel and simulated
tempering on the ferromagnetic mean-field Potts model
shown previously. We also illustrate how it causes
torpid mixing of tempering on a mixture of normal
distributions with unequal covariances in $ R^M $, a
previously unknown result with relevance to statistical
inference problems. More generally, anytime a
multimodal distribution includes both very narrow and
very wide peaks of comparable probability mass,
parallel and simulated tempering are shown to mix
slowly.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Markov chain, rapid mixing, spectral gap, Metropolis
algorithm",
}
@Article{Schertzer:2009:SPB,
author = "Emmanuel Schertzer and Rongfeng Sun and Jan Swart",
title = "Special points of the {Brownian} net",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "30:805--30:864",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-641",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/641",
abstract = "The Brownian net, which has recently been introduced
by Sun and Swart [16], and independently by Newman,
Ravishankar and Schertzer [13], generalizes the
Brownian web by allowing branching. In this paper, we
study the structure of the Brownian net in more detail.
In particular, we give an almost sure classification of
each point in $ \mathbb {R}^2 $ according to the
configuration of the Brownian net paths entering and
leaving the point. Along the way, we establish various
other structural properties of the Brownian net.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "branching-coalescing point set.; Brownian net;
Brownian web",
}
@Article{Caballero:2009:ABI,
author = "Mar{\'\i}a Caballero and V{\'\i}ctor Rivero",
title = "On the asymptotic behaviour of increasing self-similar
{Markov} processes",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "31:865--31:894",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-637",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/637",
abstract = "It has been proved by Bertoin and Caballero
{citeBC2002} that a $ 1 / \alpha $-increasing
self-similar Markov process $X$ is such that $ t^{-1 /
\alpha }X(t)$ converges weakly, as $ t \to \infty, $ to
a degenerate random variable whenever the subordinator
associated to it via Lamperti's transformation has
infinite mean. Here we prove that $ \log (X(t) / t^{1 /
\alpha }) / \log (t)$ converges in law to a
non-degenerate random variable if and only if the
associated subordinator has Laplace exponent that
varies regularly at $ 0.$ Moreover, we show that $
\liminf_{t \to \infty } \log (X(t)) / \log (t) = 1 /
\alpha, $ a.s. and provide an integral test for the
upper functions of $ \{ \log (X(t)), t \geq 0 \} $.
Furthermore, results concerning the rate of growth of
the random clock appearing in Lamperti's transformation
are obtained. In particular, these allow us to
establish estimates for the left tail of some
exponential functionals of subordinators. Finally, some
of the implications of these results in the theory of
self-similar fragmentations are discussed.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "self-similar Markov processes",
}
@Article{Meester:2009:USD,
author = "Ronald Meester and Anne Fey-den Boer and Haiyan Liu",
title = "Uniqueness of the stationary distribution and
stabilizability in {Zhang}'s sandpile model",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "32:895--32:911",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-640",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/640",
abstract = "We show that Zhang's sandpile model $ (N, [a, b]) $ on
$N$ sites and with uniform additions on $ [a, b]$ has a
unique stationary measure for all $ 0 \leq a < b \leq
1$. This generalizes earlier results of {citeanne}
where this was shown in some special cases. We define
the infinite volume Zhang's sandpile model in dimension
$ d \geq 1$, in which topplings occur according to a
Markov toppling process, and we study the
stabilizability of initial configurations chosen
according to some measure $ m u$. We show that for a
stationary ergodic measure $ \mu $ with density $ \rho
$, for all $ \rho < \frac {1}{2}$, $ \mu $ is
stabilizable; for all $ \rho \geq 1$, $ \mu $ is not
stabilizable; for $ \frac {1}{2} \leq \rho < 1$, when $
\rho $ is near to $ \frac {1}{2}$ or $1$, both
possibilities can occur.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Sandpile, stationary distribution, coupling, critical
density, stabilizability",
}
@Article{Appleby:2009:SSD,
author = "John Appleby and Huizhong Wu",
title = "Solutions of Stochastic Differential Equations obeying
the Law of the Iterated Logarithm, with applications to
financial markets",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "33:912--33:959",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-642",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/642",
abstract = "By using a change of scale and space, we study a class
of stochastic differential equations (SDEs) whose
solutions are drift--perturbed and exhibit asymptotic
behaviour similar to standard Brownian motion. In
particular sufficient conditions ensuring that these
processes obey the Law of the Iterated Logarithm (LIL)
are given. Ergodic--type theorems on the average growth
of these non-stationary processes, which also depend on
the asymptotic behaviour of the drift coefficient, are
investigated. We apply these results to inefficient
financial market models. The techniques extend to
certain classes of finite--dimensional equation.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Brownian motion; inefficient market; Law of the
Iterated Logarithm; Motoo's theorem; stationary
processes; stochastic comparison principle; stochastic
differential equations",
}
@Article{Nagahata:2009:CLT,
author = "Yukio Nagahata and Nobuo Yoshida",
title = "{Central Limit Theorem} for a Class of Linear
Systems",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "34:960--34:977",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-644",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/644",
abstract = "We consider a class of interacting particle systems
with values in $ [0, \infty)^{\mathbb {Z}^d} $, of
which the binary contact path process is an example.
For $ d \geq 3 $ and under a certain square
integrability condition on the total number of the
particles, we prove a central limit theorem for the
density of the particles, together with upper bounds
for the density of the most populated site and the
replica overlap.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "central limit theorem, linear systems, binary contact
path process, diffusive behavior, delocalization",
}
@Article{Dedecker:2009:RCM,
author = "J{\'e}r{\^o}me Dedecker and Florence Merlev{\`e}de and
Emmanuel Rio",
title = "Rates of convergence for minimal distances in the
central limit theorem underprojective criteria",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "35:978--35:1011",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-648",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/648",
abstract = "In this paper, we give estimates of ideal or minimal
distances between the distribution of the normalized
partial sum and the limiting Gaussian distribution for
stationary martingale difference sequences or
stationary sequences satisfying projective criteria.
Applications to functions of linear processes and to
functions of expanding maps of the interval are
given.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Minimal and ideal distances, rates of convergence,
Martingale difference sequences",
}
@Article{Masson:2009:GEP,
author = "Robert Masson",
title = "The growth exponent for planar loop-erased random
walk",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "36:1012--36:1073",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-651",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/651",
abstract = "We give a new proof of a result of Kenyon that the
growth exponent for loop-erased random walks in two
dimensions is 5/4. The proof uses the convergence of
LERW to Schramm--Loewner evolution with parameter 2,
and is valid for irreducible bounded symmetric random
walks on any two dimensional discrete lattice.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "loop-erased random walk; Random walk; Schramm--Loewner
evolution",
}
@Article{Hambly:2009:ENV,
author = "Ben Hambly and Lisa Jones",
title = "Erratum to {``Number Variance from a probabilistic
perspective, infinite systems of independent Brownian
motions and symmetric $ \alpha $-stable processes''}",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "37:1074--37:1079",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-658",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
note = "See \cite{Hambly:2007:NVP}.",
URL = "http://ejp.ejpecp.org/article/view/658",
abstract = "In our original paper, we provide an expression for
the variance of the counting functions associated with
the spatial particle configurations formed by infinite
systems of independent symmetric alpha-stable
processes. The formula (2.3) of the original paper, is
in fact the correct expression for the expected
conditional number variance. This is equal to the full
variance when L is a positive integer multiple of the
parameter a but, in general, the full variance has an
additional bounded fluctuating term. The main results
of the paper still hold for the full variance itself,
although some of the proofs require modification in
order to incorporate this change.",
acknowledgement = ack-nhfb,
ajournal = "Electron. J. Probab.",
fjournal = "Electronic Journal of Probability",
journal-URL = "http://ejp.ejpecp.org/",
keywords = "Number variance, symmetric $\alpha$-stable processes,
controlled variability, Gaussian fluctuations,
functional limits, long memory, Gaussian processes,
fractional Brownian motion",
}
@Article{Schuhmacher:2009:DED,
author = "Dominic Schuhmacher",
title = "Distance estimates for dependent thinnings of point
processes with densities",
journal = j-ELECTRON-J-PROBAB,
volume = "14",
pages = "38:1080--38:1116",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1214/EJP.v14-643",
ISSN = "1083-6489",
ISSN-L = "1083-6489",
bibdate = "Mon Sep 1 19:06:47 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ejp.bib",
URL = "http://ejp.ejpecp.org/article/view/643",
abstract = "In [Schuhmacher, Electron. J. Probab. 10 (2005),
165--201] estimates of the Barbour--Brown distance $
d_2 $ between the distribution of a thinned point
process and the distribution of a Poisson process were
derived by combining discretization with a result based
on Stein's method. In the present article we
concentrate on point processes that have a density with
respect to a Poisson process, for which we can apply a
corresponding result directly without the detour of
discretization. This enables us to obtain better and
more natural bounds in the $ d_2$-metric, and for the
first time also bounds in the stro
