On the concentration of Sinai's walk

被引：7
作者：
Andreoletti, Pierre [1 ]
机构：
[1] Univ Aix Marseille 2, Fac Sci Luminy, F-13288 Marseille 09, France
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2006年 / 116卷 / 10期
关键词：
random environment; random walk; Sinai's regime; Markov chain; local time;
D O I：
10.1016/j.spa.2004.12.008
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
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.
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收藏
页码：1377 / 1408
页数：32
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