时间随机环境下随机游动的渐近行为

Asymptotic Behavior for Random Walk in Random Environments

本文给出了可数状态空间中时间随机环境下随机游动的一个统一的模型 .对于最常见的情况 ,即d维最近邻域随机环境下随机游动 ,如果环境是严平稳的 ,则在一定条件下 ,该随机游动满足强大数定律和中心极限定理 .特别地 ,当环境独立同分布时 ,我们可以得到更为具体的结果 ,该结果类似于经典的随机游动的相应结论 .

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.