本文選題：可列非齊次馬氏鏈 + B-C引理　； 參考：《安徽工業(yè)大學(xué)》2015年碩士論文

【摘要】：隨機(jī)過(guò)程是一連串隨機(jī)事件動(dòng)態(tài)關(guān)系的定量描述。馬爾科夫過(guò)程作為一類重要的隨機(jī)過(guò)程,其理論基礎(chǔ)極為深厚,應(yīng)用空間也非常廣泛。它與拓?fù)鋵W(xué)、近世代數(shù)、幾何學(xué)、泛函分析和函數(shù)論等相互交叉,同時(shí)其理論成果又可以成功運(yùn)用到計(jì)算機(jī)、通信、經(jīng)濟(jì)管理等諸多領(lǐng)域。正是由于馬爾科夫過(guò)程在數(shù)值計(jì)算、信息理論、自動(dòng)控制生物科學(xué)等方面起到異乎尋常的作用,使得人們愈發(fā)重視馬爾科夫過(guò)程理論和其應(yīng)用的研究。概率論的主要分支之一就是概率極限理論,同時(shí)概率極限理論也是概率論中其它分支和數(shù)理統(tǒng)計(jì)的重要基礎(chǔ),近代概率極限理論研究的中心課題之一便是對(duì)隨機(jī)變量序列的強(qiáng)極限定理的研究。本文主要研究可列狀態(tài)下非齊次馬氏鏈部分和滑動(dòng)平均的極限性質(zhì),引入滑動(dòng)相對(duì)熵的概念,利用似然比極限性質(zhì)及分析方法相結(jié)合,對(duì)可列非齊次馬氏鏈已有的強(qiáng)極限定理做了推廣,并得到了一類用不等式表示的關(guān)于可列非齊次馬氏鏈的強(qiáng)偏差定理,推廣了部分已有結(jié)果。全書(shū)一共分為六章,第一章是緒論部分,介紹了本論文的選題背景。第二章簡(jiǎn)略的介紹了相關(guān)的基本理論和概念,以及在可列狀態(tài)下非齊次馬氏鏈極限理論中與本文有關(guān)的一些研究現(xiàn)狀。第三章得到了可列狀態(tài)下非齊次馬氏鏈的一類強(qiáng)極限定理。第四章進(jìn)一步給出了可列狀態(tài)下非齊次馬\可夫鏈泛函的一類強(qiáng)大數(shù)定律。第五章是在第三章和第四章研究的基礎(chǔ)上,進(jìn)一步研究可列狀態(tài)下三重循環(huán)馬氏鏈的漸近均分性。第六章是結(jié)束語(yǔ)與展望。
[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.
【學(xué)位授予單位】：安徽工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O211.4

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 汪忠志;楊衛(wèi)國(guó);;關(guān)于相依離散隨機(jī)序列的若干強(qiáng)偏差定理[J];系統(tǒng)科學(xué)與數(shù)學(xué);2011年08期

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本文編號(hào)：1972516