Some Properties For Random Walk With Resting State In Random Environments

Radom walk in random environments is discussed in this paper , random environments has two forms ,one is space-random enviroments,that is to say ,enviroments is random varyiable,which is change with space location ;one is time-random environments, that is to say , enviroments is random varyiable,which is to follow time fading away .This paper has three chapters ,in the frist chapter we study randon walk with resting state in space-random enviroments on the right half line,the model is given and existence is proved,at the same time we gain the recurrence criterion and weak law of large numbers of this randon walk , it is diffrent from in the case of random walk in space-random enviroments on the full line. In the second chapter a general model of random walk in time-random environments is given .Moreover,in the case of one-dimensional nearest-neighbor random walk if the environments are independent identically distributed,we derive a strong law of large numbers and a center limit theorem of this random walk under some reasonable conditions ,which are similar to the corresponding results in the case of classical random walk in space-random environments. In the third chapter ,the model,which has two aborp barriers random walk in random environments with resting state ,with the set of finite non-negative integers as state space is constructed , its existence is proved ,and absorption probabilities is obtained.