ABSTRACT
The asymptotic equipartition property is a basic theorem in information theory. In this paper, we study the strong law of large numbers of Markov chains in single-infinite Markovian environment on countable state space. As corollary, we obtain the strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for this process. Finally, we give the asymptotic equipartition property of Markov chains in single-infinite Markovian environment on countable state space.
Acknowledgments
The authors would like to thank the anonymous reviewers for their valuable comments which allow us to improve the quality of this paper significantly.
Disclosure statement
No potential conflict of interest was reported by the author.