A type of Markov approximation of random fields on a homogeneous tree and a class of small deviation theorems (Q2275789)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A type of Markov approximation of random fields on a homogeneous tree and a class of small deviation theorems |
scientific article |
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A type of Markov approximation of random fields on a homogeneous tree and a class of small deviation theorems (English)
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9 August 2011
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A class of small deviation theorems for an arbitrary bivariate function is 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 random fields on the homogeneous tree are obtained.
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Shannon-McMillan theorem
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homogeneous tree
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arbitrary random field
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Markov random field
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sample relative entropy density
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