The Existence Theorems For Sample Relative Entropy Rate And Divergence Rate Of Finite Asymptotic Circular Markov Chains

Markov process is an important probabilistic process. The limit theory for Markov chains is one of the basic areas on Markov processes'research. The research about homogeneous Markov chains has formed integrated theoretic system. The research about limit theorems, ergodic properties, entropy rate, divergence and sample relative entropy rate has been researching in recent years. In view of application in real life, transition function of inhomogeneous Markov chains is often appeared in the asymptotic circle form. The purpose of this paper is to study the existence theorems for sample relative entropy rate and divergence rate of finite asymptotic circle Markov chains.