On the concentration of Sinai's walk

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:116

Article

Andreoletti, Pierre

关键词: random environment;    random walk;    Sinai's regime;    Markov chain;    local time;   

DOI  :  10.1016/j.spa.2004.12.008

来源: Elsevier

【 摘 要 】

We consider Sinai's random walk in a random environment. We prove that for an interval of time [l, n] Sinai's walk sojourns in a small neighborhood of the point of localization for the quasi-totality of this amount of time. Moreover the local time at the point of localization normalized by n converges in probability to a well defined random variable of the environment. From these results we get applications to the favorite sites of the walk and to the maximum of the local time. (C) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

Free