Some Problems Of Ergodic For Nonhomogeneous Markov Chains

Probability theory is a subject which concerns the study statistical laws for different kinds of random phenomenon,and theoretica foundations of many applying subjects.Such as Informatin theory,Mathematics Risk theory and Insurance theory for Actuaries etc. Markov process is an important stochastic process. It has profound theoretical fundament,and extensive applied area. At present Markov chains has become very rich content of branch of mathematics. For the study for homogeneous Markov chains, many results have been obtained, which are mature enough to form a complete theoretical system.Compared with the great achievements homogeneous Markov chains has already made, nonhomogeneous Markov chains is still an important topic for futher research now. For ergodicity problem for nonhomogeneous Markov chains, researchers have done much work in recent years, such as chinese researchers Chen and Yang and so on. In this master's thesis,we shall develop this research.The main purpose of this thesis is to study some problems of ergodic for nonhomogeneous Markov chains.It has five chapters.In chapter one and two,we give an introduction of the basic notions,main results and approaches used in this paper.In chapter three,we mainly research the relationship among irreducible, C-strong ergodicity, absolute mean strong ergodic and strong ergodic through the concrete example.In chapter four, The rate of convergence of absolute mean strong ergodic for nonhomogeneous Markov chains by using the character of norm and nonhomogeneous Markov chains and the geometric ergodic for stationary Markov chains is obtained.