Analysis of random walks in dynamic random environments via L2-perturbations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Avena, L.¹  Blondel, O.²  Faggionato, A.³ 

[1] Leiden Univ, Math Inst, Postbus 9512, NL-2300 RA Leiden, Netherlands

[2] Univ Claude Bernard Lyon 1, Univ Lyon, CNRS, ICJ,UMR 5208, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France

[3] Univ Roma La Sapienza, Dipartimento Matemat, Ple Aldo Moro 2, I-00185 Rome, Italy

关键词: Perturbations of Markov processes;    Poincare inequality;    Dyson-Phillips expansion;    Random walk in dynamic random environment;    Asymptotic velocity;    Invariance principle;   

DOI  :  10.1016/j.spa.2017.11.010

来源: Elsevier

【 摘 要 】

We consider random walks in dynamic random environments given by Markovian dynamics on Z(d). We assume that the environment has a stationary distribution mu and satisfies the Poincare inequality w.r.t. mu. The random walk is a perturbation of another random walk (called unperturbed). We assume that also the environment viewed from the unperturbed random walk has stationary distribution mu. Both perturbed and unperturbed random walks can depend heavily on the environment and are not assumed to be finite-range. We derive a law of large numbers, an averaged invariance principle for the position of the walker and a series expansion for the asymptotic speed. We also provide a condition for non-degeneracy of the diffusion, and describe in some details equilibrium and convergence properties of the environment seen by the walker. All these results are based on a more general perturbative analysis of operators that we derive in the context of L-2-bounded perturbations of Markov processes by means of the so-called Dyson-Phillips expansion. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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