Several Strong Laws Of Large Numbers For Markov Chains Indexed By A Tree

In recent years,the tree model has attracted a great deal of interest among scientists from various research fields such as physics,probability theory,information theory etc..Moreover,stochastic process indexed by a tree has become a hot topic in the field of the probability theory in recent years.The research of the strong law of large numbers has held an important position in the development process of probability theory,and the strong law of large numbers is one of the central issues of the international probability theory.In this paper,through constructing non-negative martingales and applies Doob's martingale convergence theorem to the research of a.e.convergence,a class of strong laws of large numbers for Markov chain fields indexed by a tree are given.This paper includes six chapters:The first chapter is introduction,introducing the researching purpose and meanings of this paper,and the work that existed.The second chapter is preparative knowledge.We introduce the concept of the tree and give the definition of a special kind of non-homogeneous tree.In the third chapter,we give a class of Shannon-Mc Millan theorems of generalized random selection system for m-ordered non-homogeneous Markov information source on a special kind of non-homogeneous tree.In the forth chapter,we give a class of strong laws of large numbers of mordered continuous state non-homogeneous Markov chain on a special kind of non-homogeneous tree.In the fifth chapter,we give a strong limit theorem for double Markov chains on a special kind of non-homogeneous tree.In the last chapter,we sum up what we have done in this paper.