Some Limit Theorems Of Markov Chains And Markov Chain Fields On Trees

Markov processes is an important random processes, it has not only profound theoretic foundament but also extensive applied area. The research of strong limit theorem is always one of central subjects in international probability fields. This paper used martingale convergence theorem by constructing proper martingale to study some limit theorems of Markov chain and Markov chain fields on trees.This paper includes six 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 fifth are main parts. In the second chapter, a strong limit theorem of the three variables function of non-homogeneous hidden Markov model is given. In the third chapter, introducing strong law of large numbers of Markov chain fields taking values in numerable states on generalized Bethe trees. In the fourth chapter, introducing a strong limit theorem of the frequencies of occurrence of states about continuous function defined in fixed interval for the Markov chain fields on generalized Cayley trees. The fifth chapter gives main conclusions of this paper.