Copulae of probability measures on product spaces
type: Item
instance of: scholarly article
title: Copulae of probability measures on product spaces
zbMATH Open document ID: 0698.60016
DOI: 10.1016/0047-259X(89)90062-6
published in: Journal of Multivariate Analysis
publication date: 1989-01-01T00:00:00Z
review text: The author generalizes the construction of copulas given by \textit{M. Sklar} [Publ. Inst. Statist. Univ. Paris 8, 229-231 (1960; Zbl 0100.142)] to probability measures on Polish product spaces. This gives a representation of the form \[ \mu (A_ 1\times...\times A_ n)=C(P_ 1(A_ 1),...,P_ n(A_ n)) \] for a probability measure \(\mu\) with marginals \(P_ 1,...,P_ n\). As an application \textit{G. Dall'Aglio}'s [see ``Probability theory.'' (1987; Zbl 0609.60001)] characterization of the convergence in probability is generalized. Reviewer's remark: A result closely related to the main result of this paper has been proved independently in a paper by Rachev and R schendorf, to be published in Theory Probab. Appl. (1990).
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60B05
Mathematics Subject Classification ID: 60B10
zbMATH DE Number: 4145025
zbMATH Keywords: probability measures on product spaces
zbMATH Keywords: construction of copulas
zbMATH Keywords: characterization of the convergence in probability
author: Marco Scarsini
MaRDI profile type: Publication
cites work: Q5560061
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full work available at URL: 0047-259x(89)90062-6
OpenAlex ID: W1970506389
description: scientific article; zbMATH DE number 4145025