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THE STRONG LIMIT THEOREM FOR RELATIVE ENTROPY DENSITY RATES BETWEEN TWO ASYMPTOTICALLY CIRCULAR MARKOV CHAINS

Published online by Cambridge University Press:  02 April 2018

Ying Tang ,
Weiguo Yang  and
Yue Zhang
Ying Tang
Affiliation:
Faculty of Science, Jiangsu University, Zhenjiang 212013, People's Republic of China and Shanghai Normal University, Tianhua College, Shanghai 201815, China
Weiguo Yang
Affiliation:
Faculty of Science, Jiangsu University, Zhenjiang 212013, People's Republic of China E-mail: [email protected]
Yue Zhang
Affiliation:
Faculty of Science, Jiangsu University, Zhenjiang 212013, People's Republic of China E-mail: [email protected]
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Abstract

In this paper, we are going to study the strong limit theorem for the relative entropy density rates between two finite asymptotically circular Markov chains. Firstly, we prove some lammas on which the main result based. Then, we establish two strong limit theorem for non-homogeneous Markov chains. Finally, we obtain the main result of this paper. As corollaries, we get the strong limit theorem for the relative entropy density rates between two finite non-homogeneous Markov chains. We also prove that the relative entropy density rates between two finite non-homogeneous Markov chains are uniformly integrable under some conditions.

Keywords

asymptotic equipartition propertyasymptotically circular Markov chainsrelative entropy density ratestrong law of large numbers
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 2 , April 2019 , pp. 161 - 171
Copyright
Copyright © Cambridge University Press 2018 

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