On The Absolute Mean Strong Ergodicity Of Continuous-state Nonhomogeneous Markov Chains

Markov chain is a special case of stochastic process.It is widely used in production decision-making and market share of enterprises.There are many studies at home and abroad.For continuous-state nonhomogeneous Markov chains,Zhang Pengyan and Yang Weiguo have explored the strong law of large numbers of multivariate functions of continuous-state nonhomogeneous Markov chains;for absolute mean strong ergodicity,Yang Weiguo has explored the case of discrete-state nonhomogeneous Markov chains.Combining both,this paper mainly studies the absolute mean strong ergodicity of continuous-state nonhomogeneous Markov chains.The contents of this paper are divided into five parts:In the first section,the research background and significance of Markov chain and the research status at home and abroad,the research content and chapter arrangement are introduced;In the second section,the definition of discrete state Markov chains is given,and the concept of continuous state Markov chains is introduced,and the basic theory of convergence of random variables,conditional expectation and martingale involved in the following chapters are introduced;In the third section,the known theorem of discrete-state homogeneous Markov chains in recurrent state is given,and a new easy-to-understand proof of the theorem is given by using state classification and recurrent property,and a corollary is obtained;In the fourth section,firstly,the concept of absolute mean strong ergodicity of discrete-state nonhomogeneous Markov chains is given.Secondly,the definition of absolute mean strong ergodicity of continuous-state nonhomogeneous Markov chains is introduced.Then,a sufficient condition for continuous-state nonhomogeneous Markov chains to satisfy this strong ergodicity is given.Lastly,the application of this ergodicity in information theory of continuous state non-homogeneous Markov chains is given;In the fifth section,the summary and outlook is provided.