| Markov processes is an important probabilistic processes.It has profound theoretic foundament,such as topology,theory of functions, functional analysis,modern algebra and geometry,and it has extensive applied area,such as physics,chemistry,biology,astronomy,computer, communication,management of economy and so on.The study of limit theorems is the main task in propability theory.The research abouthomogeneous Markov chains has formed integrated theoretic system. Nowadays more and more researches about limit thorems and ergodic of nonhomogeneous Markov chains have been done.The definition of mth order Markov Chains is the generization of Markov chains.As the development and application of mth order Markov Chains,researchers become more and more interested in its theoretical reseach and further application.Professor Liu Wen and Professor Yang Weiguo do much work in studing the strong limit functions of markov chains and obtain fruitful results.The article mainly uses the method of martingle which is created by Professor Yang and the method of analysis to continue the work on limit theorems of markov chains.The article includes five chapters.In the first chapter,we introduce the relative background on this paper,the main methods used in this paper and what will be studied in this paper,and then give some simple expressions of the work which have been done.In the second chapter,we introduce the basic theory which needs to use in the subsequent chapters., for example,the definition and functions of martingle,of the difference of martingle,of conditional expect and Markov Chains.From the third chapter to the fifth chapter is the main part of the paper.In the third chapter, we will prove some strong limit theorems of frequency of occurrence of arbitrary k states for two order Markov Chains.The fourth chapter will generize these results to mth order Markov Chains and obtain a series of corollaries.We will give the simple sum-up about this paper in the last chapter. |
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