树指标马氏链关于泊松分布的一个强极限定理  

A Strong Limit Theorem About Poisson Distribution for Markov Chains Indexed by a Tree

作　　者：袁红星 李佳芯 刘会杰 金少华[1] 马雷雨 YUAN Hongxing;LI Jiaxin;LIU Huijie;JIN Shaohua;MA Leiyu(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》2020年第4期309-316,共8页Acta Analysis Functionalis Applicata

基　　金：河北工业大学大学生创新创业训练计划项目(X202010080049)。

摘　　要：树指标随机过程已成为近年来发展起来的概率论的研究方向之一.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.本文通过引入滑动相对熵的概念和构造非负鞅,利用Doob鞅收敛定理研究给出了非齐次树指标马氏链关于泊松分布的一个强极限定理.Stochastic process indexed by a tree has become a hot topic in the field of the probability theory in recent years.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,by introducing the concept of sliding relative entropy and constructing a non-negative martingale,a strong limit theorem about Poisson distribution for Markov chains indexed by a non-homogeneous tree is established by applying Doob’s martingale convergence theorem.

关 键 词：强极限定理 非齐次树 鞅 泊松分布 滑动相对熵 

分 类 号：O211.6[理学—概率论与数理统计]