The strong law of large numbers and Shannon-McMillan theorem for Markov chains indexed by an infinite tree with uniformly bounded degree in random environment

DOI10.1080/03610926.2019.1708398OpenAlexW3000682921MaRDI QIDQ5078569

Chengjun Ding, Zhiyan Shi, Wei-guo Yang

Publication date: 23 May 2022

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610926.2019.1708398

zbMATH Keywords

treestrong law of large numbersrandom environmentShannon-McMillan theoremuniformly bounded degree

Mathematics Subject Classification ID

Statistics (62-XX)

Related Items (1)

Shannon-McMillan theorem and strong law of large numbers for Markov chains indexed by generalized spherically symmetric trees

Cites Work

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• A Mathematical Theory of Communication
• On the central limit theorem for Markov chains in random environments
• On direct convergence and periodicity for transition probabilities of Markov chains in random environments
• Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree
• The strong ergodic theorem for densities: Generalized Shannon-McMillan- Breiman theorem
• A sandwich proof of the Shannon-McMillan-Breiman theorem
• Automorphism invariant measures on trees
• Markov chains indexed by trees
• Some limit properties for Markov chains indexed by a homogeneous tree.
• Strong law of large numbers for Markov chains field on a Bethe tree
• An extension of Shannon-McMillan theorem and some limit properties for nonhomogeneous Markov chains
• The Strong Law of Large Numbers and the Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree
• The ergodic theory of Markov chains in random environments
• The Individual Ergodic Theorem of Information Theory
• The Asymptotic Equipartition Property for<tex>$M$</tex>th-Order Nonhomogeneous Markov Information Sources
• The Asymptotic Equipartition Property for Nonhomogeneous Markov Chains Indexed by a Homogeneous Tree
• Entropic aspects of random fields on trees
• The asymptotic behavior for Markov chains in a finite i.i.d random environment indexed by cayley trees
• Strong laws of large numbers for countable Markov chains indexed by a Cayley tree
• THE SHANNON–MCMILLAN THEOREM FOR MARKOV CHAINS INDEXED BY A CAYLEY TREE IN RANDOM ENVIRONMENT
• STRONG LAW OF LARGE NUMBERS FOR MARKOV CHAINS INDEXED BY SPHERICALLY SYMMETRIC TREES
• The definition of tree-indexed Markov chains in random environment and their existence
• A Note on the Ergodic Theorem of Information Theory
• The Basic Theorems of Information Theory

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