Optimal coupling of multivariate distributions and stochastic processes
type: Item
instance of: scholarly article
title: Optimal coupling of multivariate distributions and stochastic processes
zbMATH Open document ID: 0788.60025
author: A. Tuero-Diaz
author: Juan Antonio Cuesta-Albertos
author: Ludger Rüschendorf
published in: Journal of Multivariate Analysis
publication date: 1993-12-06T00:00:00Z
review text: Let \(({\mathcal U},{\mathcal B})\) be a measure space and \((x,y)\in M(P,Q)\) be \({\mathcal U}\times {\mathcal U}\)-valued random variables in a common probability space \((\Omega,{\mathcal F},\lambda)\) with marginal distributions \(P\) and \(Q\), respectively. A pair \((x,y)\) is optimal coupling (o.c.) if the Kantorovich functional \(\sigma(P,Q)\) induced by \(\sigma: {\mathcal U}\times {\mathcal U} \to \mathbb{R}_ +\) equals to \(\int \sigma(x,y)d\lambda\). Chosen some \(\sigma\), i.e. some metric, the problem is to characterize such pairs. The authors consider minimal metrics of \(\ell_ p\)-type, spaces \(\mathbb{R}^ N\) and \(\mathbb{R}^ T\) as \(\mathcal U\) and discuss some transformations \(\varphi\) (in particular, radial transformations, positive transformations and monotone transformations of the components) for which \((x,\varphi(x))\) are o.c. pairs.
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60G99
Mathematics Subject Classification ID: 62H20
zbMATH DE Number: 445133
zbMATH Keywords: optimal coupling
zbMATH Keywords: marginal distributions
zbMATH Keywords: Kantorovich functional
reviewed by: Nijolė Kalinauskaitė
MaRDI profile type: Publication
full work available at URL: jmva.1993.1064
OpenAlex ID: W2046027298
DOI: 10.1006/JMVA.1993.1064
description: scientific article; zbMATH DE number 445133