Asymptotic Behavior for Random Walks in Time-Random Environment on $Z^1$

Abstract:

      In this paper, we give a general model of random walks in time-random environment in any countable space. Moreover, when the environment is independently identically distributed, a recurrence-transience criterion and the law of large numbers are derived in the nearest-neighbor case on $Z^1$. At last, under regularity conditions, we prove that the RWIRE $\{X_n\}$ on $Z^1$ satisfies a central limit theorem, which is similar to the corresponding results in the case of classical random walks.