We prove Sklar's theorem in infinite dimensions via a topological argument
and the notion of inverse systems.Comment: 6 page

Benth, Fred Espen

Di Nunno, Giulia

Schroers, Dennis

English

arXiv

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

A Topological Proof of Sklar's Theorem in Arbitrary Dimensions

Abstract

Similar works

Full text

Available Versions

NORA - Norwegian Open Research Archives