A Class of Shannon-McMillan Theorems for Nonhomogeneous Markov Chains Field Indexed by a Homogeneous Tree

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New Zealand Journal of Mathematics

Vol. 41, (2011), Pages 43-53


Kangkang Wang

School of Mathematics and physics,

Jiangsu University of Science and Technology,

Zhenjiang 212003,

China

mailto:wkk.cn@126.com






Abstract In this paper, a class of Shannon-McMillan theorems for the nonhomogeneous Markov chains field on a homogeneous tree are discussed by constructing a nonnegative martingale. As corollaries, some Shannon-Mcmillan theorems for the homogeneous Markov chains field on a homogeneous tree and the nonhomogeneous Markov chain are obtained. A result which has been obtained is extended.

Keywords Shannon-McMillan theorem, the homogeneous tree, Markov random field, relative entropy density..

Classification (MSC2000) 60F15.

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