Discrete-time random motion in a continuous random medium

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Boldrighini, C.¹  Minlos, R. A.²  Pellegrinotti, A.³ 

[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

[2] Russian Acad Sci, Inst Problems Informat Transmiss, Moscow 117901, Russia

[3] Univ Roma Tre, Dipartimento Matemat, I-00146 Rome, Italy

关键词: Random walk;    Random environment;    Central limit theorem;   

DOI  :  10.1016/j.spa.2009.05.007

来源: Elsevier

【 摘 要 】

We propose a discrete-time random walk on R(d), d = 1, 2,..., as a variant of recent models of random walk on Z(d) in a random environment which is i.i.d. in space-time. We allow space correlations of the environment and develop an analytic method to deal with them. We prove, under some general assumptions, that if the random term is small, a quenched (i.e., for a fixed history of the environment) Central Limit Theorem for the displacement of the random walk holds almost-surely. Proofs are based on L(2) estimates. We consider for brevity only the case of odd dimension d, as even dimension requires somewhat different estimates. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free