A Class of Shannon-McMillan Theorems for Nonhomogeneous Markov Chains Field Indexed by a Homogeneous Tree
New Zealand Journal of Mathematics
Vol. 41, (2011), Pages 43-53
School of Mathematics and physics,
Jiangsu University of Science and Technology,
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.