The Markov approximation of the random fields on Cayley trees and a class of small deviation theorems.

DOI10.1016/S0167-7152(03)00058-0zbMath1116.60343OpenAlexW2052699556MaRDI QIDQ1423190

Liying Wang, Wen Liu

Publication date: 14 February 2004

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-7152(03)00058-0

zbMATH Keywords

deviation theoremMarkov chain fields on Cayley treesSample relative entropy rateSmallStrong deviation theoremStrong limit theorem

Mathematics Subject Classification ID

Strong limit theorems (60F15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Measures of information, entropy (94A17)

Related Items (9)

A CLASS OF SMALL DEVIATION THEOREMS FOR FUNCTIONALS OF RANDOM FIELDS ON A TREE WITH UNIFORMLY BOUNDED DEGREE IN RANDOM ENVIRONMENT ⋮ A class of small deviation theorems for the random fields on an \(m\) rooted Cayley tree ⋮ Markov approximation of arbitrary random field on homogeneous trees ⋮ A class of small deviation theorems for functionals of random fields on double Cayley tree in random environment ⋮ New gaps between zeros of fourth-order differential equations via Opial inequalities ⋮ A class of small deviation theorems for random fields on a uniformly bounded tree ⋮ Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging ⋮ A class of small deviation theorems for functionals of random fields on a homogeneous tree ⋮ A class of small deviation theorems for Markov chains in bi-infinite random environment

Cites Work

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• Markov random fields on an infinite tree
• Markov chains indexed by trees
• The Markov approximation of the sequences of \(N\)-valued random variables and a class of small deviation theorems.
• An extension of Shannon-McMillan theorem and some limit properties for nonhomogeneous Markov chains
• Entropic aspects of random fields on trees

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