STRONG LAW OF LARGE NUMBERS FOR MARKOV CHAINS INDEXED BY SPHERICALLY SYMMETRIC TREES

DOI10.1017/S0269964815000108zbMath1370.60056MaRDI QIDQ5358055

Shi Zhiyan, Yang Weiguo, Peng Weicai

Publication date: 19 September 2017

Published in: Probability in the Engineering and Informational Sciences (Search for Journal in Brave)

Mathematics Subject Classification ID

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

Related Items (10)

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 and Shannon-McMillan theorem for Markov chains indexed by an infinite tree with uniformly bounded degree in random environment ⋮ A class of small deviation theorems for functionals of random fields on double Cayley tree in random environment ⋮ Shannon-McMillan theorem and strong law of large numbers for Markov chains indexed by generalized 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 ⋮ Tree-indexed Markov chains in random environment and some of their strong limit properties

Cites Work

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• A class of small deviation theorems for random fields on a uniformly bounded tree
• Some Shannon-McMillan approximation theorems for Markov chain field on the generalized Bethe tree
• Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree
• Automorphism invariant measures on trees
• Markov chains indexed by trees
• Some limit properties for Markov chains indexed by a homogeneous tree.
• The Asymptotic Equipartition Property for Nonhomogeneous Markov Chains Indexed by a Homogeneous Tree
• Entropic aspects of random fields on trees
• SOME STRONG LIMIT THEOREMS FOR MARKOV CHAIN FIELDS ON TREES
• Strong law of large numbers and Shannon-McMillan theorem for Markov chains field on Cayley tree

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