Every ``lower psi-mixing'' Markov chain is ``interlaced rho-mixing''
type: Item
instance of: scholarly article
title: Every ``lower psi-mixing'' Markov chain is ``interlaced rho-mixing''
zbMATH Open document ID: 0948.60064
DOI: 10.1016/S0304-4149(97)00090-2
published in: Stochastic Processes and their Applications
publication date: 2000-03-01T00:00:00Z
review text: The importance of mixing conditions for the central limit theory of weakly dependent random sequences is known, but the implications between various mixing conditions are not yet well established. The aim of the paper is to prove that for real-valued Markov chains, \(\psi '\)-mixing (a weaker version of \(\psi \)-mixing) implies \(\rho^*\)-mixing (an ``interlaced'' version of \(\rho \)-mixing). It is conjectured (but not proved) that every \(\varphi \)-mixing sequence (not even Markovian or stationary) is \(\rho ^*\)-mixing. A detailed discussion of mixing properties and implications is included.
reviewed by: Ivan Saxl
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60G07
zbMATH DE Number: 1409159
zbMATH Keywords: Markov chain
zbMATH Keywords: \(\psi '\)-mixing
zbMATH Keywords: \(\rho ^*\)-mixing
author: Richard C. Bradley
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1409159