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Recent
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Volume 52
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3
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4
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Volume 51
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Volume 50
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Volume 49
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Volume
48
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Vietnam
Journal of Mathematics 39:1 (2011) 1-17
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A Type of Markov Approximation of Random Fields on
a Homogeneous Tree
and a Class
of Small Deviation Theorems
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Kangkang Wang and
Mingxing Zhu
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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.
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2000 Mathematics Subject Classification: 60F15.
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Keywords: Shannon-McMillan theorem, the homogeneous
tree, arbitrary random field, Markov random field, sample
relative entropy density.
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Established
by Vietnam Academy of Science and Technology &
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Published by
Springer since January 2013
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