Copulas and Markov processes
type: Item
instance of: scholarly article
title: Copulas and Markov processes
zbMATH Open document ID: 0770.60019
author: William F. Darsow
author: Elwood T. Olsen
author: Bao Gia Nguyen
published in: Illinois Journal of Mathematics
publication date: 1993-02-10T00:00:00Z
review text: For any real-valued random variables \(X\) and \(Y\) with joint distribution \(H\), \textit{A. Sklar} [Kybernetika, Praha 9, 449-460 (1973; Zbl 0292.60036)] showed that there is a cuopla \(C\) such that \(H(x,y)=C(F(x),G(y))\), where \(F\) and \(G\) are the marginal distributions of \(X\) and \(Y\) and \(H\) is their joint distribution. Consequently, copulas carry complete information on dependency relations between \(X\) and \(Y\). The authors define a new binary operation on the set of copulas, study its algebraic properties, and show how this operation can be used to study Markov processes. This approach to Markov processes is quite different from the standard approach. Instead of giving an initial distribution and the transition probabilities, all the marginal distributions and a family of copulas satisfying the authors' conditions are specified.
Mathematics Subject Classification ID: 60E99
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 60G07
zbMATH DE Number: 119922
zbMATH Keywords: copulas
zbMATH Keywords: complete information on dependency relations
zbMATH Keywords: binary operation on the set of copulas
reviewed by: Robert M. Tardiff
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 119922