Studies Of Strong Laws Of Large Numbers For Non-Homogeneous Markov Chain Fields On A Non-Homogeneous Tree

In recent years,the tree model has attracted a great deal of interest a-mong scientists from various research fields such as physics,probability the-ory,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 stronglaw of large numbers has held an important po-sition 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. conver-gence,a class of strong laws of large numbers for Markov chain fields on a non-homogeneous 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-McMillan theorem-s of m-ordered non-homogeneous Markov information source on a non-homogeneous tree.In the forth chapter, we give some strong deviation theorems for geomet-ric mean of the random sequence on a non-homogenous tree.In the fifth chapter, we give a class strong deviation about discrete sliding relative entropy source.In the last chapter, we sum up what we have done in this paper.