Some limit properties for Markov chains indexed by a homogeneous tree.
type: Item
instance of: scholarly article
title: Some limit properties for Markov chains indexed by a homogeneous tree.
zbMATH Open document ID: 1068.60045
published in: Statistics \& Probability Letters
publication date: 2004-02-14T00:00:00Z
review text: The author studies tree-indexed Markov chains (TIMC) which are the particular case of a Markov random field on a tree. TIMC were introduced by \textit{I. Benjamini} and \textit{Y. Peres} [Ann. Probab. 22, 219--243 (1994; Zbl 0793.60080)], who investigated the recurrence and ray-recur\-rence for them. Many aspects of TIMC have been studied before, for example, the existence of entropy rate for some stationary random fields on a homogeneous tree, a mixing property, a weak law of large numbers, the Shannon-McMillan theorem with convergence in probability for a PPG-invariant and ergodic random field on a homogeneous tree. In this paper, the local convergence theorem for countable Markov chains indexed by a homogeneous tree is studied. Also, the strong law of large numbers and the Shannon-McMillan theorem with a.e. convergence for finite Markov chains indexed by a homogeneous tree are obtained.
reviewed by: Anatoliy Swishchuk
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 2041555
zbMATH Keywords: local convergence
zbMATH Keywords: strong law of large numbers
author: Weiguo Yang
MaRDI profile type: Publication
full work available at URL: j.spl.2003.04.001
OpenAlex ID: W2042061274
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DOI: 10.1016/J.SPL.2003.04.001
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description: scientific article; zbMATH DE number 2041555