Some Shannon-McMillan approximation theorems for Markov chain field on the generalized Bethe tree

DOI10.1155/2011/470910zbMath1223.60057OpenAlexW1992949404WikidataQ59267125 ScholiaQ59267125MaRDI QIDQ535516

Kang-Kang Wang, Decai Zong

Publication date: 13 May 2011

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

Full work available at URL: https://eudml.org/doc/224778

zbMATH Keywords

entropyrandom fieldMarkov chainrooted treeShannon-McMillan theoremuniform equipartition property

Mathematics Subject Classification ID

Random fields (60G60) Trees (05C05) Stochastic network models in operations research (90B15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (4)

Shannon-McMillan theorem and strong law of large numbers for Markov chains indexed by generalized spherically symmetric trees ⋮ STRONG LAW OF LARGE NUMBERS FOR MARKOV CHAINS INDEXED BY SPHERICALLY SYMMETRIC TREES ⋮ Conditional entropy, entropy density, and strong law of large numbers for generalized controlled tree-indexed Markov chains ⋮ Some strong limit theorems for nonhomogeneous Markov chains indexed by controlled trees

Cites Work

• Some limit properties of random transition probability for second-order nonhomogeneous Markov chains indexed by a tree
• Some limit properties for Markov chains indexed by a homogeneous tree.
• An extension of Shannon-McMillan theorem and some limit properties for nonhomogeneous Markov chains
• The Asymptotic Equipartition Property for Nonhomogeneous Markov Chains Indexed by a Homogeneous Tree
• Entropic aspects of random fields on trees
• Strong law of large numbers and Shannon-McMillan theorem for Markov chain fields on trees
• SOME STRONG LIMIT THEOREMS FOR MARKOV CHAIN FIELDS ON TREES
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