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SOME STRONG LIMIT THEOREMS FOR MARKOV CHAIN FIELDS ON TREES

Published online by Cambridge University Press:  01 July 2004

Wen Liu  and
Weiguo Yang
Wen Liu
Affiliation:
Department of Mathematics, Hebei University of Technology, Tianjin 300130, China
Weiguo Yang
Affiliation:
Faculty of Science, Jiangsu University, Zhenjiang 212013, China, E-mail: wgyang@ujs.edu.cn
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Abstract

In this article, we introduce the notion of the Markov chain fields on the generalized Bethe trees or generalized Cayley trees, and some strong limit theorems on the frequencies of states and ordered couples of states, including the Shannon–McMillan theorem on Bethe tree TB,N and Cayley tree TC,N, are obtained. In the proof, a new technique in the study of the strong limit theorem in probability theory is applied.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 18 , Issue 3 , July 2004 , pp. 411 - 422
Copyright
© 2004 Cambridge University Press

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References

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