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Invariance Principles for Ranked Excursion Lengths and Heights
Csaki, Endre; A. Rényi Institute of Mathematics, Hungarian Academy of Sciences - Hu, Yueyun; Universite Paris VI

Formato:	Peer-reviewed Article,
Enlaces:	In this note we prove strong invariance principles between ranked excursion lengths and heights of a simple random walk and those of a standard Brownian motion. Some consequences concerning limiting distributions and strong limit theorems will also be presented.
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

A Condition for Weak Disorder for Directed Polymers in Random Environment
Birkner, Matthias; Weierstrass Institute for Applied Analysis and Stochastics, Germany

Formato:	Peer-reviewed Article,
Enlaces:	We give a sufficient criterion for the weak disorder regime of directed polymers in random environment, which extends a well-known second moment criterion. We use a stochastic representation of the size-biased law of the partition function.
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

Recurrent Graphs where Two Independent Random Walks Collide Finitely Often
Krishnapur, Manjunath; University of California at Berkeley, USA - Peres, Yuval; University of California at Berkeley, USA

Formato:	Peer-reviewed Article,
Enlaces:	We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely. In particular, the comb lattice, obtained from $Z^2$ by removing all horizontal edges off the $x$-axis, has…
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

Poisson Statistics for the Largest Eigenvalues of Wigner Random Matrices with Heavy Tails
Soshnikov, Alexander; University of California at Davis, USA

Formato:	Peer-reviewed Article,
Enlaces:	We study large Wigner random matrices in the case when the marginal distributions of matrix entries have heavy tails. We prove that the largest eigenvalues of such matrices have Poisson
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

A Gaussian Oscillator
Burdzy, Krzysztof; University of Washington - White, David; University of Washington

Formato:	Peer-reviewed Article,
Enlaces:	We present a stochastic process with sawtooth paths whose distribution is given by a simple rule and whose stationary distribution is Gaussian. The process arose in a natural way in research on interaction of an inert particle with a Brownian…
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

Sharp Bounds for Green and Jumping Functions of Subordinate Killed Brownian Motions
Song, Renming; University of Illinois, Urbana - Vondracek, Zoran; University of Zagreb, Croatia

Formato:	Peer-reviewed Article,
Enlaces:	In this paper we obtain sharp bounds for the Green function and jumping function of a subordinate killed Brownian motion in a bounded $C^{1,1}$ domain, where the subordinating process is a subordinator whose Laplace exponent has certain asymptotic behavior at…
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

Geometric Ergodicity and Perfect Simulation
Kendall, Wilfrid S.; University of Warwick

Formato:	Peer-reviewed Article,
Enlaces:	This note extends the work of Foss and Tweedie (1998), who showed that availability of the classic Coupling from the Past (CFTP) algorithm of Propp and Wilson (1996) is essentially equivalent to uniform ergodicity for a Markov chain (see also…
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

On Standard Normal Convergence of the Multivariate Student $t$-Statistic for Symmetric Random Vectors
Giné, Evarist; University of Connecticut, USA - Götze, Friedrich; Universitat Bielefeld

Formato:	Peer-reviewed Article,
Enlaces:	It is proved that if the multivariate Student $t$-statistic based on i.i.d. symmetric random vectors is asymptotically standard normal, then these random vectors are in the generalized domain of attraction of the normal law. Uniform integrability is also considered, even…
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

Weak Convergence to Ocone Martingales: a Remark
Peccati, Giovanni; Universite Pierre et Marie Curie, France

Formato:	Peer-reviewed Article,
Enlaces:	We show, by a simple counterexample, that the main result in a recent paper by H. Van Zanten [Electronic Communications in Probability 7 (2002), 215-222] is false. We eventually point out the origin of the error.
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

10.

On Long Range Percolation with Heavy Tails
Friedli, Sacha; IMPA, Rio de Janeiro - Borge de Lima, Benoîte; UFMG, Belo Horizonte - Sidoravicius, Vladas; IMPA, Rio de Janeiro

Formato:	Peer-reviewed Article,
Enlaces:	Consider independent long range percolation on $\mathbf{Z}^d$, $d\geq 2$, where edges of length $n$ are open with probability $p_n$. We show that if $\limsup_{n\to\infty}p_n > 0,$ then there exists an integer $N$ such that $P_N(0\leftrightarrow \infty) > 0$, where $P_N$…
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

11.

State Tameness: A New Approach for Credit Constrains
Londono, Jaime A.; Universidad EAFIT

Formato:	Peer-reviewed Article,
Enlaces:	We propose a new definition for tameness within the model of security prices as  Itô processes that is risk-aware.  We give a new definition for arbitrage and characterize it.  We then prove a theorem that can be seen as an…
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

12.

Large Deviations for Mixtures
Biggins, J. D.; The University of Sheffield, UK

Formato:	Peer-reviewed Article,
Enlaces:	The results discussed here are most easily described in words using Bayesian terminology. For each $n$, there are probability distributions for the data conditional on a parameter, and there is also a prior distribution for the parameter. Integrating out, using…
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

13.

Oscillation and Non-oscillation in Solutions of Nonlinear Stochastic Delay Differential Equations
Appleby, John A. D.; Dublin City University - Kelly, Conall; Dublin City University, Dublin, Ireland

Formato:	Peer-reviewed Article,
Enlaces:	This paper studies the oscillation and nonoscillation of solutions of a nonlinear stochastic delay differential equation, where the noise perturbation depends on the current state, and the drift depends on a delayed argument. When the restoring force towards equilibrium is…
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

14.

Ergodicity of PCA: Equivalence between Spatial and Temporal Mixing Conditions
Louis, Pierre-Yves; Technische Universitat Berlin

Formato:	Peer-reviewed Article,
Enlaces:	For a general attractive Probabilistic Cellular Automata on $S^{\mathbb{Z}^d}$, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition ($\mathcal{A}$). This condition means the exponential decay…
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

15.

A Bound for the Distribution of the Hitting Time of Arbitrary Sets by Random Walk
Jarai, Antal A; Carleton University, Canada - Kesten, Harry; Cornell University

Formato:	Peer-reviewed Article,
Enlaces:	We consider a random walk $S_n = \sum_{i=1}^n X_i$ with i.i.d. $X_i$. We assume that the $X_i$ take values in $\Bbb Z^d$, have bounded support and zero mean. For $A \subset \Bbb Z^d, A \ne \emptyset$ we define $\tau_A =…
Fecha:	2004-01-01
Recurso:	Electronic communications in probability

Recurso libre

16.

The scaling limit of senile reinforced random walk.
Holmes, Mark P; University of Auckland

Formato:	Peer-reviewed Article,
Enlaces:	This paper proves that the scaling limit of nearest-neighbour senile reinforced random walk is Brownian Motion when the time T spent on the first edge has finite mean. We show that under suitable conditions, when T has heavy tails the…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

17.

A note on new classes of infinitely divisible distributions on $\mathbb{R}^d$
Maejima, Makoto; Keio University - Nakahara, Genta; Keio University

Formato:	Peer-reviewed Article,
Enlaces:	This paper introduces and studies a family of new classes of infinitely divisible distributions on $\mathbb{R}^d$ with two parameters. Depending on parameters, these classes connect the Goldie-Steutel-Bondesson class and the class of generalized type $G$ distributions, connect the Thorin class…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

18.

A note on r-balayages of matrix-exponential L'evy processes
Sheu, Yuan-Chung; Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan - Chen, Yu-Ting; Institute of Mathematics, Academia Sinica, Taipei, Taiwan

Formato:	Peer-reviewed Article,
Enlaces:	In this note we give semi-explicit solutions for $r$-balayages of matrix-exponential-Lévy processes. To this end, we turn to an identity for the joint Laplace transform of the first entry time and the undershoot and a semi-explicit solution of the negative…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

19.

Berry-Esseen Bounds for Projections of Coordinate Symmetric Random Vectors
Goldstein, Larry; University of Southern California - Shao, Qi-Man; Hong Kong University of Science and Technology

Formato:	Peer-reviewed Article,
Enlaces:	For a coordinate symmetric random vector $(Y_1,\ldots,Y_n)={\bf Y} \in \mathbb{R}^n$, that is, one satisfying $(Y_1,\ldots,Y_n)=_d(e_1Y_1,\ldots,e_nY_n)$ for all $(e_1,\ldots,e_n) \in \{-1,1\}^n$, for which $P(Y_i=0)=0$ for all $i=1,2,\ldots,n$, the following Berry Esseen bound to the cumulative standard normal $\Phi$ for the standardized…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability