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THE SHANNON–MCMILLAN THEOREM FOR MARKOV CHAINS INDEXED BY A CAYLEY TREE IN RANDOM ENVIRONMENT

Published online by Cambridge University Press:  29 December 2017

Zhiyan Shi,
Pingping Zhong and
Yan Fan
Zhiyan Shi
Affiliation:
Faculty of Science, Jiangsu University, Zhenjiang 212013, China E-mail: shizhiyan1984@126.com
Pingping Zhong
Affiliation:
Faculty of Science, Jiangsu University, Zhenjiang 212013, China and Jingjiang College of Jiangsu University, Zhenjiang 212013, China E-mail: zpp2008@126.com
Yan Fan
Affiliation:
Jingjiang College of Jiangsu University, Zhenjiang 212013, China E-mail: free1002@126.com
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Abstract

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In this paper, we give the definition of tree-indexed Markov chains in random environment with countable state space, and then study the realization of Markov chain indexed by a tree in random environment. Finally, we prove the strong law of large numbers and Shannon–McMillan theorem for Markov chains indexed by a Cayley tree in a Markovian environment with countable state space.

Keywords

Markov chainsrandom environmentShannon–McMillan theoremstrong law of large numbers

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 4 , October 2018, pp. 626 - 639
Copyright
Copyright © Cambridge University Press 2017 

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