非齐次树上非齐次马氏链的一类强偏差定理  

A Class of Strong Deviation Theorems of Non-homogeneous Markov Chains on a Non-homogeneous Tree

作　　者：金少华[1] 赵旋[1] 王东[2] 刘伟娜[1] JIN Shaohua ZHAO Xuan WANG Dong LIU Weina(College of Science, Hebei University of Technology, Tianjin 300401, China Hebei University of Technology Langfang Branch, Langfang 065000, China)

机构地区：[1]河北工业大学理学院,天津300401 [2]河北工业大学廊坊分校,廊坊065000

出　　处：《应用泛函分析学报》2016年第3期266-273,共8页Acta Analysis Functionalis Applicata

基　　金：河北省高等学校科学技术研究重点项目(ZD2014051)

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.强偏差定理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,给出了一类非齐次树上m阶非齐次马氏链的一类强偏差定理.In recent years, tree indexed stochastic process has become one of the hot topics in probability theory. The strong deviation theorem has been one of the central issues of the international probability theory. In this paper, through constructing a non-negative martingale and applying Doob＇s martingale convergence theorem to the research of a.e. convergence, a class of strong deviation theorems of m-ordered nonhomogeneous Markov chains on a non-homogeneous tree are given.

关 键 词：非齐次树 鞅 马氏链 强偏差定理 

分 类 号：O177.91[理学—数学]