THE SHANNON–MCMILLAN THEOREM FOR MARKOV CHAINS INDEXED BY A CAYLEY TREE IN RANDOM ENVIRONMENT

DOI10.1017/S0269964817000444zbMath1506.60070OpenAlexW2777039047MaRDI QIDQ5050862

Pingping Zhong, Zhiyan Shi, Yan Fan

Publication date: 18 November 2022

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

Full work available at URL: https://doi.org/10.1017/s0269964817000444

zbMATH Keywords

Markov chainsstrong law of large numbersrandom environmentShannon-McMillan theorem

Mathematics Subject Classification ID

Trees (05C05) Discrete-time Markov processes on general state spaces (60J05) Strong limit theorems (60F15) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Processes in random environments (60K37)

Related Items (7)

A CLASS OF SMALL DEVIATION THEOREMS FOR FUNCTIONALS OF RANDOM FIELDS ON A TREE WITH UNIFORMLY BOUNDED DEGREE IN RANDOM ENVIRONMENT ⋮ 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 ⋮ Some generalized strong limit theorems for Markov chains in bi-infinite random environments ⋮ 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 generalized entropy ergodic theorem for nonhomogeneous bifurcating Markov chains indexed by a binary tree ⋮ Tree-indexed Markov chains in random environment and some of their strong limit properties

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