可列非齐次马氏链的极限定理

发布时间：2018-06-03 10:50

本文选题：可列非齐次马氏链 + B-C引理　；参考：《安徽工业大学》2015年硕士论文

【摘要】：随机过程是一连串随机事件动态关系的定量描述。马尔科夫过程作为一类重要的随机过程,其理论基础极为深厚,应用空间也非常广泛。它与拓扑学、近世代数、几何学、泛函分析和函数论等相互交叉,同时其理论成果又可以成功运用到计算机、通信、经济管理等诸多领域。正是由于马尔科夫过程在数值计算、信息理论、自动控制生物科学等方面起到异乎寻常的作用,使得人们愈发重视马尔科夫过程理论和其应用的研究。概率论的主要分支之一就是概率极限理论,同时概率极限理论也是概率论中其它分支和数理统计的重要基础,近代概率极限理论研究的中心课题之一便是对随机变量序列的强极限定理的研究。本文主要研究可列状态下非齐次马氏链部分和滑动平均的极限性质,引入滑动相对熵的概念,利用似然比极限性质及分析方法相结合,对可列非齐次马氏链已有的强极限定理做了推广,并得到了一类用不等式表示的关于可列非齐次马氏链的强偏差定理,推广了部分已有结果。全书一共分为六章,第一章是绪论部分,介绍了本论文的选题背景。第二章简略的介绍了相关的基本理论和概念,以及在可列状态下非齐次马氏链极限理论中与本文有关的一些研究现状。第三章得到了可列状态下非齐次马氏链的一类强极限定理。第四章进一步给出了可列状态下非齐次马\可夫链泛函的一类强大数定律。第五章是在第三章和第四章研究的基础上,进一步研究可列状态下三重循环马氏链的渐近均分性。第六章是结束语与展望。
[Abstract]:Stochastic process is a quantitative description of the dynamic relationship of a series of random events. As an important stochastic process, Markov process has a very deep theoretical foundation and wide application space. It intersects with topology, modern algebra, geometry, functional analysis and function theory. At the same time, its theoretical achievements can be successfully applied to many fields such as computer, communication, economic management and so on. It is because Markov process plays an extraordinary role in numerical computation, information theory, automatic control biological science and so on, that people pay more attention to the research of Markov process theory and its application. One of the main branches of probability theory is the theory of probability limit. At the same time, the theory of probability limit is also an important basis of other branches and mathematical statistics in probability theory. One of the central topics of modern probability limit theory is the study of strong limit theorems for random variable sequences. In this paper, the limit properties of nonhomogeneous Markov chain and moving average are studied. The concept of sliding relative entropy is introduced, and the likelihood ratio limit property is combined with the analytical method. In this paper, we generalize the strong limit theorems of listed nonhomogeneous Markov chains, and obtain a class of strong deviation theorems for listed nonhomogeneous Markov chains represented by inequalities, which generalize some of the existing results. The book is divided into six chapters, the first chapter is the introduction, introduced the background of this paper. In the second chapter, the basic theories and concepts are briefly introduced, as well as some research status in the limit theory of nonhomogeneous Markov chains in the countable state. In chapter 3, we obtain a class of strong limit theorems for nonhomogeneous Markov chains in countable states. In chapter 4, we give a class of strong law of large numbers for nonhomogeneous horse chain Functionals in a countable state. In chapter 5, on the basis of the studies in chapters 3 and 4, we further study the asymptotic homogeneity of triple cyclic Markov chains in the countable state. Chapter six is the conclusion and prospect.
【学位授予单位】：安徽工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O211.4

【参考文献】