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SOME STRONG LIMIT THEOREMS FOR MARKOV CHAIN FIELDS ON TREES
Published online by Cambridge University Press: 01 July 2004
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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