Some Properties Of Random Walks In Random Environments

Random walks in random environments is a special example ofMarkov chains in random environments.This paper is composed of threechapters:in the first chapter,we introduce the construction of Markovchains in random environments;the second chapter is divided into twoparts,one gives the model of random walks in random environments onthe whole line,and a su?cient and necessary condition of null recurrenceis equivalent;In the other part,the model on the half line is given,undersome special conditions,we prove a strong law of large numbers,and weapply it to discuss its recurrence and nonrecurrence.In the last one,weintroduce recurrent sets and transient sets of skew product Markovchains,and discuss some criterions for judging states,additionally,we findan invariant measure and show some properties.