On the Lin condition in strong ratio limit theorems
type: Item
instance of: scholarly article
title: On the Lin condition in strong ratio limit theorems
zbMATH Open document ID: 1056.60026
published in: Mathematical Notes
publication date: 2004-12-07T00:00:00Z
review text: Let \((X_n,n\geq 0)\) be a Markov chain with state space \((E,{\mathcal B})\) and \(P\) be a transition operator. It is proved that for a wide class of Markov chains and, in particular, for many random walks on groups the formula (Lin condition) \(\liminf (v(P^{n+1}f)/ v(P^nf))=1\) holds, where \(v\) and \(f\) are a probability measure on \({\mathcal B}\) and a \({\mathcal B}\)-measurable function, respectively.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60J05
zbMATH DE Number: 2121432
zbMATH Keywords: Markov chains
zbMATH Keywords: random walks on groups
zbMATH Keywords: multistep transition probability
author: M. G. Shur
MaRDI profile type: Publication
full work available at URL: b:matn.0000030995.23171.d6
OpenAlex ID: W1971894853
DOI: 10.1023/B:MATN.0000030995.23171.D6
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description: scientific article; zbMATH DE number 2121432