树上非齐次马氏链转移矩阵的若干极限性质  

Many limit properties of transition matrix for a nonhomogeneous Markov chain indexed by a tree

作　　者：金少华[1] 于凯丽 任双双 李小雪[1] 

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《纯粹数学与应用数学》2017年第6期551-559,共9页Pure and Applied Mathematics

基　　金：河北工业大学研究生矩阵论示范课程建设项目(121031)

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发展起来的概率论的研究方向.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.本文通过引入样本散度的概念,通过构造适当的非负鞅,将Doob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重可列非齐次马氏链转移矩阵的若干极限性质.In recent years, the tree model has attracted a great deM 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 researh 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 introducing the concept of sample divergence rate , constructing non-negative martingale and applies Doob＇s martingale convergence theorem to the research of a.e. convergence, many limit properties of transition matrix for m-ordered countable non-homogeneous Markov chains on a non-homogeneous tree are obtained.

关 键 词：非齐次树 鞅 马氏链 强极限定理 

分 类 号：O177.91[理学—数学]