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Some Strong Deviation Theorems for Markov Chain Fields on A Tree

Author: ZhangYanMin
Tutor: JinShaoHua
School: Hebei University of Technology
Course: Applied Mathematics
Keywords: non-homogeneous tree strong deviation theorem the sample divergence generating function random sum Martingale Markov chains
CLC: O211.62
Type: Master's thesis
Year: 2011
Downloads: 4
Quote: 0
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Abstract


During recent decades,the tree model has gained great concerns among scien-tists from various research fields such as physics,probability theory,informationtheory etc..Moreover,stochastic process indexed by a tree has become a hot topicin the field of the probability theory in recent years. On the other hand, the re-search of the deviation theorem has held an important position in the developmentprocess of probability theory, and the strong deviation theorem is one of the cen-tral issues of the international probability theory.In this paper, through constructing non-negative martingales and applies Doob’smartingale convergence theorem to the research of a.e. convergence, some strongdeviation theorems for Markov chain fields on a tree are given. This paper in-cludes six chapters:The first chapter is introduction, introducing the researching purpose and mean-ings of this paper, and the work that existed.The second chapter is preparative knowledge. We give the concept of the treeand the definition of a kind of non-homogeneous tree.In the third chapter, we first give a class of strong deviation theoremswith respect to m-ordered non-homogeneous Markov chains on a kind of non-homogenous tree.As corollaries,we give some strong deviation theorems for theentropy density and the frequency of occurrence of the states with respect to m-ordered non-homogeneous Markov chains on a kind of non-homogenous tree.In the forth chapter, a class of random approximation theorems for randomsums on a kind of non-homogenous tree are obtained by using the tools of theconditional generating functions and the tailed-probability generating function.In the fifth chapter, we give the strong deviation theorem for functional of con-tinuous state Markov chains on a kind of non-homogeneous tree.In the last chapter, we sum up what we have done in this paper.

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory ) > Random process > Markov process
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