Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 470910, 18 pages
doi:10.1155/2011/470910
Research Article

Some Shannon-McMillan Approximation Theorems for Markov Chain Field on the Generalized Bethe Tree

Kangkang Wang1 and Decai Zong2

1School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang 212003, China
2College of Computer Science and Engineering, Changshu Institute of Technology, Changshu 215500, China

Received 26 September 2010; Accepted 7 January 2011

Academic Editor: Józef Banaś

Copyright © 2011 Kangkang Wang and Decai Zong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A class of small-deviation theorems for the relative entropy densities of arbitrary random field on the generalized Bethe tree are discussed by comparing the arbitrary measure 𝜇 with the Markov measure 𝜇 𝑄 on the generalized Bethe tree. As corollaries, some Shannon-Mcmillan theorems for the arbitrary random field on the generalized Bethe tree, Markov chain field on the generalized Bethe tree are obtained.