The Convergence And Convergence Rate Of Nonhomogeneous Markov Chains

Markov processes is an important probabilistic processes.It has profound theoretic foundament ,such as topology,theory of functions,functional analysis,modem algebra and geometry,and it has extensive applied area,such as physics, chemistry, biology, astronomy, computer,communication,management of economy.The research about homogeneous Markov chains has formed integrated theoretic system;The research about nonhomogeneous Markov chain has been researching.This article is going to study the convergence and rate of convergence about nonhomogeneous Markov chains.In the first chapter,we introduce the 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 rate of convergence of nonhomogeneous Markov chains and the absolute average strong ergodic.Firstly,based on the B.Bowerman's result about the rate of convergence in Cesaro sense of certain nonhomogeneous Markov chains which the transition matrices converge,we are to study a certain nonhomogenous Markov chains which the transition matrices average converge to a period strongly ergodic stochastic matrice,and control the average convergenc rate of transition matrices,then we get the rate of convergence in Cesaro sense about the nonhomogeneous Markov chains by used the character of norm and the character of nonhomogeneous Markov chains.It is an extension of a B.Bowerman's result.We also discuss the application on the expected average cost.And then we quote the concept of absolute average strong ergodic which YangWeiguo has introduced.We give the equivalence between the absolute average strong ergodic and strong ergodic for homogeneous Markov chains.And we give sufficient condition of absolute average strong ergodic for a nonhomogeneous Markov chains through injecting another nonhomogeneous Markov chains which is strong ergodic,which is an extension of YangWeiguo's result aboutabsolute average strong ergodic for a nonhomogeneous Markov chains.In the fourth chapter,we quoted a normal matrix,and proved a convergence theorem about nonhomogeneous Markov chains.The theorem is an extension of Yang Weiguo's Cesaro average convergence theorem of nonhomengeous Markov chains.