Limit Properties For Divergence Of Markov Processes

Markov processes is an important probabilistic process.It has profound theoretic foundation,such as topology,theory of functions, functional analysis,modern algebra and geometry.In addition,it has extensive applied areas,such as physics,chemistry,biology,astronomy, computer,communication and management of economy.The research about homogeneous Markov chains has formed integrated theoretic system.The research about limit theorems and ergodic properties has been researching in recent years.The definition of mth-order nonhomogeneous Markov chains is an extension of the definition of Markov chains.Mth-order Markov information source is an important information source.So the research about the theory of nonhomogeneous Markov chains is very important.This article is going to study the limit properties for divergence of Markov processes and mth-order Markov processes.In the first chapter,we introduce the audiovisual definition,relative research and progresses about Markov chains.In the second chapter,we introduce the basic theory which needs to use in the subsequent chapters. In the third chapter,we study the limit properties for the divergence of Markov processes.Firstly,Yang weiguo and Liu Wen studied the asymptotic equipartition properties for Markov information,based on the uniform integrability of random variable sequences,we are to give the limit properties for the divergence of Markov processes,and then we compute the limit.In the fourth chapter,we introduce the basic theories of finite mth-order nonhomogeneous Markov chains on the basis of the second chapter,which is the preparation of the next.Finally,we discuss the limit properties for the divergence for finite mth-order Markov chains.In this section,we mainly based on the results on the asymptotic equipartition property for mth-order nonhomogeneous Markov information source given by Yang weiguo and Liu Wen,we study the limit properties for the divergence for finite mth-order Markov chains, generalizing the results in the third chapter.