变化环境中分枝树上有偏随机游动的状态分类

Classification of states for a biased random walk on a branching tree in the varying environment

考虑变化环境中分枝树上的广义有偏随机游动,分别得到随机游动为暂留的、正常返的和零常返的充分条件,为进一步研究这类随机游动的中心极限定理等性质做了铺垫。

In this study we investigate biased random walk on branching trees in the varying environment. We have obtained the sufficient conditions for transience,positive recurrence,and null recurrence. Our main result enables the further study on the central limit theory for this kind of random walks.