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作者：Holroyd, AE
作者单位：University of California System; University of California Los Angeles
摘要：We study the effects of boundary conditions in two-dimensional rigidity percolation. Specifically, we consider generic rigidity in the bond percolation model on the triangular lattice. We introduce a theory of boundary conditions and define two different notions of ''rigid clusters,'' called r(0)-clusters and r(1)-clusters, which correspond to free boundary conditions and wired boundary conditions respectively. The definition of an r(0)-cluster turns out to be equivalent to the definition of a...
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作者：Borkovec, M; Klüppelberg, C
作者单位：Technical University of Munich
摘要：We consider the class of autoregressive processes with ARCH(1) errors given by the stochastic difference equation X-n = alphaX(n-1) + rootbeta + lambdaX(n-1)(2) epsilon(n), nis an element of N where (epsilon(n))(nepsilonN) are i.i.d. random variables, Under general and tractable assumptions we show the existence and uniqueness of a stationary distribution. We prove that the stationary distribution has a Paretu-like tail with a well-specified tail index which depends on alpha, lambda and the di...
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作者：Ignatiouk-Robert, I
作者单位：CY Cergy Paris Universite
摘要：In this paper we prove the local sample path large deviation estimates for a general class of Markov chains with discontinuous statistics. The local rate function is represented in terms of the convergence parameter of associated local transform matrices. Our method is illustrated by the case of perturbated random walks in Z(d).
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作者：Mazza, C; Piau, D
作者单位：Universite Claude Bernard Lyon 1
摘要：We use McFadden's integral equations for random RC filters to study the average distribution of Dubins-Freedman processes. These distributions are also stationary probability measures of Markov chains on [0, 11, defined by the iteration of steps to the left x --> u x, and of steps to the right x - v + (1 - v) x, where u and v are random from [0, 1]. We establish new algorithms to compute the stationary measure of these chains. Turning to specific examples, we show that, if the distributions of...
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作者：Nuzman, CJ; Poor, HV
作者单位：Alcatel-Lucent; Lucent Technologies; AT&T; Princeton University
摘要：It has recently been observed that wide-sense self-similar processes have a rich linear structure analogous to that of wide-sense stationary processes. In this paper, a reproducing kernel Hilbert space (RKHS) approach is used to characterize this structure. The RKHS associated with a self-similar process on a variety of simple index sets has a straightforward description, provided that the scale-spectrum of the process can be factored. This RKHS description makes use of the Mellin transform an...
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作者：Gouet, R; López, FJ
作者单位：Universidad de Chile; Universidad de Chile; University of Zaragoza
摘要：We consider Z as an infinite lattice street where cars of integer length in greater than or equal to 1 can park. The parking process is described by a 0-1 interacting particle system such that a site Z E if is in state 1 whenever a car has its rear end at z and 0 otherwise. Cars attempt to park after exponential times with parameter lambda, leave after exponential times with parameter 1and are not allowed to touch nor overlap. We define and study a jamming occupation density for this parking p...
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作者：Bertsimas, D; Gamarnik, D; Tsitsiklis, JN
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); International Business Machines (IBM); IBM USA; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We study the distribution of steady-state queue lengths in multiclass queueing networks under a stable policy. We propose a general methodology based on Lyapunov functions for the performance analysis of infinite state Markov chains and apply it specifically to Markovian multiclass queueing networks. We establish a deeper connection between stability and performance of such networks by showing that if there exist linear or piece-wise linear Lapunov functions that show stability, then these Lya...
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作者：Chen, X
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：The exact convergence rates of the particle distributions in supercritical branching random walks and supercritical branching Wiener processes are obtained and a conjecture of Revesz is confirmed.
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作者：Klebaner, FC; Liptser, R
作者单位：University of Melbourne; Tel Aviv University
摘要：A stochastic Lotka-Volterra model is formulated by using the semi-martingale approach. The large deviation principle is established, and is used to obtain a bound for the asymptoties of the time to extinction of prey population. The bound is given in terms of past-dependent ODEs closely related to the dynamics of the deterministic Lotka-Volterra model.
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作者：Del Moral, P; Miclo, L
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：A path-valued interacting particle systems model for the genealogical structure of genetic algorithms is presented, We connect the historical process and the distribution of the whole ancestral tree with a class of Feynman-Kac formulae on path space. We also prove increasing and uniform versions of propagation of chaos for appropriate particle block size and time horizon yielding what seems to be the first result of this type for this class of particle systems.
