非齐次树上可列非齐次马氏链集间转移的一类强大数定律  

A Class of Strong Laws of Large Numbers About Countable Non-Homogeneous Markov Chain Transferring Between Sets on a Non-Homogenous Tree

作　　者：赵秀梅 李佳芯 袁红星 刘会杰 金少华[1] ZHAO Xiumei;LI Jiaxin;YUAN Hongxing;LIU Huijie;JIN Shaohua(College of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]河北工业大学理学院

出　　处：《应用泛函分析学报》2019年第3期217-224,共8页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11701139)

摘　　要：近年来树模型已引起物理学、概率论及信息论界的广泛兴趣.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,对强大数定律的研究一直占重要地位,强大数定律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Doob鞅收敛定理应用于几乎处处收敛的研究,研究给出了一类非齐次树上可列非齐次马氏链集间转移的一类强大数定律.In recent years,the tree model has attracted a great deal of interest among scientists from various research fields such as physics,probability theory,information theory etc..Moreover,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 laws of large numbers has held an important position in the development process of probability theory,and the strong law of large numbers 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,a class of strong laws of large numbers about countable non-homogeneous Markov chain transferring between sets on a non-homogenous tree are given.

关 键 词：非齐次树 鞅 马尔科夫链 强大数定律 

分 类 号：O211.6[理学—概率论与数理统计]