随机游动轨道中的分枝结构  

Branching structure within random walk

作　　者：王华明 张琳[2] 张美娟[3] 洪文明[4] Huaming Wang;Lin Zhang;Meijuan Zhang;Wenming Hong

机构地区：[1]安徽师范大学数学与统计学院,芜湖241003 [2]北京邮电大学理学院,北京100876 [3]中央财经大学统计与数学学院,北京100081 [4]北京师范大学数学科学学院,北京100875

出　　处：《中国科学：数学》2019年第3期517-534,共18页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11501008;11801596和11131003)资助项目

摘　　要：随机游动是一类经典的随机过程.利用母函数等分析方法,已有丰富且深入的研究.而基于对(紧邻)随机游动轨道分解而得到的内在分枝结构,是研究非(空间)齐次随机游动的基本工具.这一方法首先被Kesten等(1975)用于研究随机环境中紧邻随机游动,得到游动深刻的极限性质.对于非紧邻情形,一直没有建立游动相应的内在分枝结构.本文综述了近年来作者在这方面的研究工作,建立了有界跳幅及带形上随机游动的内在分枝结构,并应用分枝结构得到相应随机游动的极限性质.Random walk is one of the most classical stochastic processes.It has been extensively studied by using analysis methods such as the probability generating function,and there are abundant research results about it.The intrinsic branching structure within the(nearest-neighborhood)random walk,which can be obtained by decomposing the path of the walk,serves as a powerful tool to study the state-dependent random walk.This approach was firstly used by Kesten et al.(1975)to study the nearest-neighborhood random walk in a random environment to get a nice stable limit theorem.So it is attractive to set up the intrinsic branching structures for non-nearest-neighborhood random walks which have been unsolved for a long time.We devote the paper to giving a survey of our results in recent years on the intrinsic branching structures within the random walk with bounded jumps and the random walk on a strip,along with some limit properties of the random walk which we develop by using this approach.

关 键 词：分枝结构 随机游动 首中时 

分 类 号：O211.6[理学—概率论与数理统计]