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Some Strong Laws of Large Numbers for Markov Chain Fields on a Tree

Author: LvJie
Tutor: JinShaoHua
School: Hebei University of Technology
Course: Applied Mathematics
Keywords: non-homogeneous trees Martingale difference sequence hiddenMarkov model strong law of large numbers Markov information source Shannon-McMillan theorem
CLC: O211.4
Type: Master's thesis
Year: 2011
Downloads: 5
Quote: 0
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Abstract


Markov process is a very important class of stochastic process．It plays an ex—gaordmary role in many fields．During recent years，the tree model has attractedextensive interest in the fields of physics，probability theory and mfomlation the—ory etc．．Markov chain indexed by a tree is a special stochastic field．Actuallyit is a stochastic walk mdexed by a tree．In recent years，tree indexed stochasticprocess has become one of the research directions for studymg in the probabilitytheory．The stronglaw oflargenumbers has been one ofthe centralissues oftheinternational probability theory．By constructing martingale difference sequences，this issue apply martingaledifference sequence convergence theorem to give and prove some trong laws oflarge numbers．The contents of this paper is divided into six chapters：The first chapter is mtroduction，describing the researching pmpose，signifi—cance and the work mat existed．The second chapter is preparative knowledge．We introduct the concept of thetree and give the definition of a special kind of non—homogeneous tree．In the third chapter，we give some s~ong limit theorems of random transformofhidden Markov model on the non—homogeneous tree．In the forth chapter，we give some s~ong deviation theorems of the F—distribution for a non—homogeneous tree of module 111．In the fifth chapter，we give Shannon—McMillan theorem of non—homogeneousMarkov information source on the non—homogeneous tree of module 111．In the last chapter，we summarize the main results of this paper．

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