A class of small deviation theorems for the random fields on an \(m\) rooted Cayley tree

DOI10.1186/1029-242X-2012-1zbMath1274.60101OpenAlexW2102001023WikidataQ59290662 ScholiaQ59290662MaRDI QIDQ366180

Zhiyan Shi, Lixin Tian, Wei-guo Yang, Wei-Cai Peng

Publication date: 12 September 2013

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1029-242x-2012-1

zbMATH Keywords

strong deviation theoremShannon-McMillan theorem\(m\) rooted Cayley tree\(m\)th-order nonhomogeneous Markov chain

Mathematics Subject Classification ID

Strong limit theorems (60F15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

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Cites Work

• Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree
• Some limit properties for the \(m\)th-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree
• Automorphism invariant measures on trees
• Markov chains indexed by trees
• Some limit properties for Markov chains indexed by a homogeneous tree.
• The Markov approximation of the random fields on Cayley trees and a class of small deviation theorems.
• Strong law of large numbers for Markov chains field on a Bethe tree
• The Asymptotic Equipartition Property for<tex>$M$</tex>th-Order Nonhomogeneous Markov Information Sources
• Entropic aspects of random fields on trees

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