树指标m重非齐次马氏信源的一个强大数定律  

A Strong Law of Large Numbers for m-ordered Non-homogeneous Markov Information Source Indexed by a Tree

作　　者：金少华[1] 袁红星 李佳芯 刘会杰 马雷雨 王卓佳 JIN Shao-hua;YUAN Hong-xing;LI Jia-xin;LIU Hui-jie;MA Lei-yu;WANG Zhuo-jia(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：《数学的实践与认识》2020年第18期209-216,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11701139);2020年河北工业大学大学生创新创业重点项目(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.将经典的一重非齐次马氏信源上的强大数定律推广到树指标m重非齐次马氏信源上,以拓展强大数定律的适用范围.通过引入相对熵密度偏差的概念和构造非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,研究给出了关于树上m重非齐次马氏信源的一个强大数定律.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.The purpose of this paper is to extend the classical strong laws of large numbers on 1-ordered nonhomogeneous Markov information source to m-ordered nonhomogeneous Markov information source indexed by a tree,so as to extend the application scope of the strong laws of large numbers.In this paper,by introducing the concept of relative entropy density deviation and constructing a non-negative martingale,and applying Doob’s martingale convergence theorem to the research of a.e.convergence,a strong law of large numbers for m-ordered nonhomogeneous Markov information source indexed by a tree is established.

关 键 词：强大数定理 非齐次树 鞅 马氏信源 概率空间 

分 类 号：O211.6[理学—概率论与数理统计]