【作者】 兰景涛；

【导师】 金少华；

【作者基本信息】 河北工业大学 ， 应用数学， 2007， 硕士

【摘要】 马尔可夫过程是一类重要的随机过程，它有极为深厚的理论基础，又有广泛的应用空间。强极限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鞅，利用鞅收敛定理研究了马尔可夫链及树上马尔可夫链场的若干极限定理本论文共分六章，第一章是绪论，介绍本论文的选题背景并对已有的工作进行扼要的介绍；第二、三、四章是本论文的主体，分别讨论隐非齐次马尔可夫模型三元泛函的强极限定理、广义Bethe树图上可数状态马氏链场的局部收敛定理、Cayley树上马尔可夫链场的状态出现频率关于特定区间上的连续函数的强极限定理。第五章列出主要结论。。更多还原

【Abstract】 Markov processes is an important random processes, it has not only profound theoretic foundament but also extensive applied area. The research of strong limit theorem is always one of central subjects in international probability fields. This paper used martingale convergence theorem by constructing proper martingale to study some limit theorems of Markov chain and Markov chain fields on trees.This paper includes six chapters. The first chapter is introduction, introducing background of choosing the subject in this paper and the work that existed. The chapters from the second to the fifth are main parts. In the second chapter, a strong limit theorem of the three variables function of non-homogeneous hidden Markov model is given. In the third chapter, introducing strong law of large numbers of Markov chain fields taking values in numerable states on generalized Bethe trees. In the fourth chapter, introducing a strong limit theorem of the frequencies of occurrence of states about continuous function defined in fixed interval for the Markov chain fields on generalized Cayley trees. The fifth chapter gives main conclusions of this paper.更多还原