The Shannon–McMillan theorem for Markov chains in Markovian environments indexed by homogeneous trees

DOI10.1080/03610926.2017.1388405OpenAlexW2763522312MaRDI QIDQ5075562

Zhiyan Shi, Wei-guo Yang, Hui Lin Huang

Publication date: 16 May 2022

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

Full work available at URL: https://doi.org/10.1080/03610926.2017.1388405

zbMATH Keywords

Markov chainCayley treeShannon-McMillan theoremMarkovian environmentstrong law of large number

Mathematics Subject Classification ID

Strong limit theorems (60F15) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items (1)

A class of small deviation theorems for functionals of random fields on double Cayley tree in random environment

Cites Work

• Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree
• Markov chains in random environments: The case of Markovian environments
• Automorphism invariant measures on trees
• Markov random fields on an infinite tree
• 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
• The Asymptotic Equipartition Property for Nonhomogeneous Markov Chains Indexed by a Homogeneous Tree
• Entropic aspects of random fields on trees
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The Shannon–McMillan theorem for Markov chains in Markovian environments indexed by homogeneous trees