Asymptotic Behavior for Random Walk in Random Environments

A general model of random walk in time-random environments in any denumerable space is given in this paper.Moreover,in the case of d-dimensional nearest-neighbor random walk,if the environments are stationary,we derive a strong law of large numbers and a center limit theorem of this random walk under some reasonable conditions.Especially,when the environments are independent identically distributed,more exact results are given,which are similar to the corresponding results in the case of classical random walk.