The asymptotic equipartition property of Markov chains in single infinite Markovian environment on countable state space

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.

KEYWORDS:

• Strong law of large numbers
• asymptotic equipartition property
• Markovian environment
• Markov chains

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 60J10
• 60F15

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.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (11601191, 11571142), Youth talent cultivation project of Jiangsu University, Young science and technology talents lifting project of Jiangsu association for science and technology.