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Vietnam Journal of Mathematics 39:1 (2011) 1-17

  

A Type of Markov Approximation of Random Fields on a Homogeneous Tree

 and a Class of Small Deviation Theorems

Kangkang Wang and Mingxing Zhu

 

Abstract. In this paper, a class of small deviation theorems for an arbitrary bivariate function are introduced by introducing the sample relative entropy rate as a measure of deviation between the arbitrary random field and the Markov chains field on the homogeneous tree. As corollaries, a class of small deviation theorems for the frequencies of states ordered couples and a Shannon-McMillan approximation theorem for arbitrary ran-dom fields on the homogeneous tree are obtained.

2000 Mathematics Subject Classification: 60F15.

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

 

 

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