The Strong Law of Large Numbers and the Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree

DOI10.1109/TIT.2015.2404310zbMath1359.94312OpenAlexW2082378481WikidataQ114084358 ScholiaQ114084358MaRDI QIDQ2978669

Publication date: 28 April 2017

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1109/tit.2015.2404310

Mathematics Subject Classification ID

Measures of information, entropy (94A17) Applications of graph theory to circuits and networks (94C15) Statistical aspects of information-theoretic topics (62B10)

Related Items (17)

Strong deviation theorems for general information sources ⋮ THE SHANNON–MCMILLAN THEOREM FOR MARKOV CHAINS INDEXED BY A CAYLEY TREE IN RANDOM ENVIRONMENT ⋮ A CLASS OF SMALL DEVIATION THEOREMS FOR FUNCTIONALS OF RANDOM FIELDS ON A TREE WITH UNIFORMLY BOUNDED DEGREE IN RANDOM ENVIRONMENT ⋮ Strong law of large numbers for generalized sample relative entropy of non homogeneous Markov chains ⋮ The strong law of large numbers for non homogeneous M-bifurcating Markov chains indexed by a M-branch Cayley tree ⋮ Strong law of large numbers of the delayed sums for Markov Chains indexed by a Cayley tree ⋮ 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 ⋮ A class of strong deviation theorems for the sequence of real valued random variables with respect to continuous-state non-homogeneous Markov chains ⋮ Equivalent properties for the bifurcating Markov chains indexed by a binary tree ⋮ Some generalized strong limit theorems for Markov chains in bi-infinite random environments ⋮ A class of strong deviation theorems for the random fields associated with bifurcating Markov chains indexed by a binary tree ⋮ On strong limit theorems for general information sources with an application to AEP ⋮ A class of small deviation theorems for functionals of random fields on double Cayley tree in random environment ⋮ The asymptotic equipartition property of Markov chains in single infinite Markovian environment on countable state space ⋮ The generalized entropy ergodic theorem for nonhomogeneous bifurcating Markov chains indexed by a binary tree ⋮ An analogue of topological sequence entropy for Markov hom tree-shifts ⋮ Tree-indexed Markov chains in random environment and some of their strong limit properties

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