直线上时间随机环境下随机游动的渐近性质

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

中文关键词:  时间随机环境随机游动  常返暂留准则  强大数定律  中心极限定理.

英文关键词:Random walks in time-random environment  recurrence-transience criteria  strong law of large numbers  central limit theorem.

中文摘要:

      在状态空间是可数情形下,本文给出了时间随机环境下随机游动的一个一般模型.随后,在环境是独立同分布情形下得到了直线上时间随机环境下紧邻随机游动的一个常返与暂留准则和强大数定律;最后讨论了其中心极限定理,它类似与简单随机游动的相应结果.

英文摘要:

      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.