Shift-coupling
type: Item
instance of: scholarly article
title: Shift-coupling
zbMATH Open document ID: 0769.60062
DOI: 10.1016/0304-4149(93)90034-2
author: David Aldous
author: Hermann Thorisson
published in: Stochastic Processes and their Applications
publication date: 1993-05-16T00:00:00Z
review text: Let \(X,X',Y,Y'\) be discrete time stochastic processes. The pair \((Y,Y')\) is a coupling of \(X\) and \(X'\) if \(Y\) has the same distribution as \(X\) and \(Y'\) has the same distribution as \(X'\). A pair \((S,T)\) of random times is a shift coupling if \(Y_{S+n}=Y_{T+n}'\) for \(n=0,1,2,\dots\). This extends the usual couplings where \(S=T\), a further extension is given to coupling with respect to \(\sigma\)-fields. The authors show that shift-coupling is related to invariant \(\sigma\)- fields similar to the way that coupling is related to tail \(\sigma\)- fields. Also, couplings are considered that are maximal in the sense that the tails of the coupling time distribution provide sharp upper bounds on the distance of the \(X\)- and \(X'\)-distributions.
reviewed by: Rudolf Grübel
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 60G07
zbMATH DE Number: 167124
zbMATH Keywords: harmonic functions
zbMATH Keywords: tail sigma-fields
zbMATH Keywords: coupling
zbMATH Keywords: shift-coupling
zbMATH Keywords: coupling time distribution
MaRDI profile type: Publication
full work available at URL: 0304-4149(93)90034-2
OpenAlex ID: W4213088112
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description: scientific article; zbMATH DE number 167124