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STRONG LAW OF LARGE NUMBERS FOR MARKOV CHAINS INDEXED BY SPHERICALLY SYMMETRIC TREES

Published online by Cambridge University Press:  16 April 2015

Peng Weicai ,
Yang Weiguo  and
Shi Zhiyan
Peng Weicai
Affiliation:
Department of Mathematics, Chaohu University, Chaohu, 238000, People's Republic of China E-mail: weicaipeng@126.com
Yang Weiguo
Affiliation:
Faculty of Science, Jiangsu University, Zhenjiang, 212013, People's Republic of China
Shi Zhiyan
Affiliation:
Faculty of Science, Jiangsu University, Zhenjiang, 212013, People's Republic of China
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Abstract

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In this paper, we main consider spherically symmetric tree T. First, under the condition lim supn→∞ |T(n)|/|Ln|<∞, we investigate the strong law of large numbers (SLLNs) for T-indexed Markov chains on the nth level of T. Then, combining the Stolz theorem, we obtain the SLLNs on T. Finally, we get Shannon–McMillan theorem for T-indexed Markov chains. The obtained theorems are generalizations of some known results on Cayley tree TC, N and Bethe tree TB, N.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 3 , July 2015 , pp. 473 - 481
Copyright
Copyright © Cambridge University Press 2015 

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