Some Strong Deviation Theorems For Markov Chain Fields By A Kind Of Non-Homogeneous Tree

Random fields on tree are applications of random process on tree-a new math-matical model, which developed from coding and encoding problem in information theory.Assuming there is one sequence,whether the occurrence frequency of state and the couple states obey the large number law is the key of a good coding and encoding method,so this domain is always being a researching emphases for most scholars. In the history of the development of probability theory, the studing of the strong deviation theorems is in an important position. The strong deviation theorems is one of the central questions for studying Probability theory.This paper includes four chapters.The first chapter is introduction,introducing background of choosing the subject in this paper and the work that existed. The chapters from the second to the third are main parts, some strong deviation theorems for Markov chain fields on a kind of non-homogeneous tree were given. In the proving, a class of strong deviation theorems for Markov chain were studied by constructing a non-negative supermartingale and using the martingale convergence theorem. Furthermore,strong deviation theorem was extended to two orders Markov chains. Some strong deviation theorems of the frequency of occurrence of 3-tuple of states for arbitrary countable two orders Markov chains on a special non-homogeneous tree are obtained. In the last chapter, we summed up what we have done in this paper.