Many Researches Of Strong Limit Theorems For Markov Chain Fields Indexed By A Tree

probability theory is the science of deduction and induction of statistical rules of random phenomena,and it is a mathematical subject that studies the objective laws of random phenomena.In the development of probability theory,the research on the strong law of large numbers has always occupied an important position.Stochastic process indexed by a tree has become a hot topic in the field of the probability theory in recent years.The strong law of large numbers is one of the central issues of the international proba-bility 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 meaning of this paper,and the work that existed.In the second chapter,the concept of general tree and the definition of a special non-homogeneous tree are introduced.In the third chapter,we give a class of strong deviation theorems about the distribution of discrete exponential for Markov chain field on a special kind of non-homogeneous tree.In the fourth chapter,we give a strong deviation theorem of m-ordered continuous state non-homogeneous Markov chains on a special kind of non-homogeneous tree.In the fifth chapter,a class of strong laws of large numbers of m-ordered continuous state Markov chain on a special kind of non-homogeneous tree are given.The sixth chapter summarizes the main research results of this paper.