A topological proof of Sklar’s theorem in arbitrary dimensions

Benth Fred Espen (), Nunno Giulia Di () and Schroers Dennis ()
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Benth Fred Espen: Department of Mathematics, University of Oslo, P. O. Box 1053 Blindern, N-0316 Oslo, Norway
Nunno Giulia Di: Department of Mathematics, University of Oslo, P. O. Box 1053 Blindern, N-0316 Oslo, Norway
Schroers Dennis: Department of Mathematics, University of Oslo, P. O. Box 1053 Blindern, N-0316 Oslo, Norway

Dependence Modeling, 2022, vol. 10, issue 1, 22-28

Abstract: Copulas are appealing tools in multivariate probability theory and statistics. Nevertheless, the transfer of this concept to infinite dimensions entails some nontrivial topological and functional analytic issues, making a deeper theoretical understanding indispensable toward applications. In this short work, we transfer the well-known property of compactness of the set of copulas in finite dimensions to the infinite-dimensional framework. As an application, we prove Sklar’s theorem in infinite dimensions via a topological argument and the notion of inverse systems.

Keywords: Copulas; Sklar’s theorem; topological inverse limits; infinite dimensions; compactness (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:10:y:2022:i:1:p:22-28:n:1

DOI: 10.1515/demo-2022-0103

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