树指标m重非齐次马氏链的一类强极限定理  

Many Strong Limit Theorems for Tree Indexed m-Ordered Non-Homogeneous Markov Chains

作　　者：刘旭升[1] 全明雪 姚星旭 金少华[1] 李小雪[1] LIU Xusheng;QUAN Mingxue;YAO Xingxu;JIN Shaohua;LI Xiaoxue(College of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《应用泛函分析学报》2018年第3期295-300,共6页Acta Analysis Functionalis Applicata

基　　金：河北工业大学"大学生创新创业训练计划"创新训练项目(201710080201)

摘　　要：在概率论的发展过程中,对强极限定理的研究一直占重要地位,强极限定理也一直是国际概率论界研究的中心课题之一.本文通过构造适当的非负鞅,将鞅收敛定理应用于几乎处处收敛的研究,给出了非齐次树上m重非齐次马氏链的一类强极限定理.The research of the strong limit theorem has held an important position in the development process of probability theory, and the strong limit theorem is one of the central issues of the international probability theory. In this paper, through constructing non-negative martingales and applies Doob＇s martingale convergence theorem to the research of a.e. convergence, many strong limit theorems for m-ordered non-homogeneous Markov chains on a non-homogeneous tree are given.

关 键 词：强极限定理 马氏链 非齐次树 鞅 

分 类 号：O177.91[理学—数学]