Several Strong Deviation Theorems For Markov Chains Indexed By Trees

In recent years, the tree model has attracted a great deal of interest among scientists from various research fields such as physics, probability theory and information theory etc.. Moreover, stochastic process indexed by a tree has become a hot topic in the field of probability theory in recent years. On the other hand, the strong deviation theorem 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 deviation theorems for Markov chain fields on a special kind of 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 some strong deviation theorems of the entropy density of r-ordered continuous Markov information source on a special kind of non-homogeneous tree.In the forth chapter, we give a class of strong limit theorems for m-ordered non-homogeneous Markov chain on a special kind of non-homogeneous tree.In the fifth chapter, we give some strong laws of large numbers of m-ordered continuous state non-homogeneous Markov chain on a special kind of non-homogeneous tree.In the last chapter, we sum up what we have done in this paper.