The Limit Behavior Of Random Walks In Random Environments

Markov chain in random environments.which developed in recent years,has become an active branch of stochastic processes. It has deep realistic background and potential application. We study random walks in random environments in this dissertation.In chapter one, we introduce basic concepts and current development of Markov chain in random environments,especially backgroud of this dissertation .In the last section of this chapter,we summarize the main result of this thesis.In chapter two,we study random walks in radom environments in resting case and obtain the bound of maximal excursion and the maximum reached,using the approaches of Deheuvels.P and Revesz.P.In chapter three,we generalize random walks on half line in random environment which was first studied by Golosov by adding a resting state to a new model.The approches of Zeitouni are used to derive our main results,which including the recurrence-transience crite-rion(positive recurrence,zero recurrence and transience),the weak law of large numbers,the LDP and the probability of absorption.