树上随机游动的常返性与首回时的矩  

Recurrence and moment of first return time for the discrete-time random walks on trees

作　　者：姚柳全 李泽翔 肖恺 王颖喆[1] YAO Liuquan;LI Zexiang;XIAO Kai;WANG Yingzhe(School of Mathematical Sciences,Key Laboratory of Mathematics and Complex Systems,Ministry of Education,Beijing Normal University,100875,Beijing,China)

机构地区：[1]北京师范大学数学科学学院数学与复杂系统教育部重点实验室,北京100875

出　　处：《北京师范大学学报（自然科学版）》2020年第1期9-15,共7页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11871103)。

摘　　要：研究树上离散时间的随机游动,给出了常返、遍历及零常返的判定定理.证明了一类特殊的树上随机游动与相应的生灭过程在零常返情形下,首回时矩有限的临界阶数是等价的.Discrete-time random walks on trees are discussed in this work. Criterion theorems are presented for recurrence, ergodicity and null recurrence. For one type special null recurrent random walk on trees, it is proved that moments of first return time is equivalent to that of birth-death chains.

关 键 词：树上的随机游动 生灭链 常返 零常返 首回时的矩 

分 类 号：O211.6[理学—概率论与数理统计]