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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
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.
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- 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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