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A NOTE ON RÉNYI'S ENTROPY RATE FOR TIME-INHOMOGENEOUS MARKOV CHAINS

Published online by Cambridge University Press:  05 December 2018

Wenxi Li  and
Zhongzhi Wang Open the ORCID record for Zhongzhi Wang [Opens in a new window]
Wenxi Li
Affiliation:
School of Mathematics and Physics, Anhui University of Technology Ma'anshan, 243002China E-mail: [email protected]
Zhongzhi Wang
Affiliation:
School of Mathematics and Physics, Anhui University of Technology Ma'anshan, 243002China E-mail: [email protected]
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Abstract

In this note, we use the Perron–Frobenius theorem to obtain the Rényi's entropy rate for a time-inhomogeneous Markov chain whose transition matrices converge to a primitive matrix. As direct corollaries, we also obtain the Rényi's entropy rate for asymptotic circular Markov chain and the Rényi's divergence rate between two time-inhomogeneous Markov chains.

Keywords

Rényi's entropy rateRényi's divergence ratetime-inhomogeneous Markov chainPerron–Frobenius theorem
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 4 , October 2019 , pp. 579 - 590
Copyright
Copyright © Cambridge University Press 2018 

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