树指标m重Markov链转移矩阵的一个强极限定理  

A Strong Limit Theorem for the Transition Matrix of m-Ordered Markov Chains Indexed by a Tree

作　　者：金少华[1] 田雪然 赵秀梅 JIN Shaohua;TIAN Xueran;ZHAO Xiumei(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3期156-163,共8页Acta Analysis Functionalis Applicata

基　　金：河北省研究生示范课程建设项目(KCJSX2019011)。

摘　　要：树模型近年来已引起物理学、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.本文通过构造非负鞅,利用鞅论研究给出了非齐次树指标m重连续状态马氏链转移矩阵的一个强极限定理.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 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 constructing a nonnegative martingale and applying martingale theory,a strong limit theorem for the transition matrix of m-ordered continuous state Markov chains indexed by a non-homogeneous tree is established.

关 键 词：非齐次树 马氏链 强极限定理 鞅 概率密度函数 

分 类 号：O211.6[理学—概率论与数理统计]