One-dimensional finite range random walk in random medium and invariant measure equation

被引：15

作者：

Bremont, Julien ^{[1
]}

机构：

[1] Univ Paris Est, Fac Sci & Technol, Lab Anal & Math Appl, F-94010 Creteil, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2009年 / 45卷 / 01期

关键词：

Finite range Markov chain; Lyapunov eigenvector; Invariant measure; Stable cone; RANDOM ENVIRONMENT; RECURRENCE; TRANSIENCE;

D O I：

10.1214/07-AIHP150

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 a model of random walks on Z with finite range in a stationary and ergodic random environment. We first provide a fine analysis of the geometrical properties of the central left and right Lyapunov eigenvectors of the random matrix naturally associated with the random walk, highlighting the mechanism of the model. This allows us to formulate a criterion for the existence of the absolutely continuous invariant measure for the environments seen from the particle. We then deduce a characterization of the non-zero-speed regime of the model.

引用

页码：70 / 103

页数：34

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