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Copulas in Hilbert spaces

Research output: Contribution to journalArticlepeer-review

Erika Hausenblas, Markus Riedle

Original languageEnglish
Pages (from-to)1-18
Number of pages18
Early online date16 Mar 2016
Accepted/In press23 Feb 2016
E-pub ahead of print16 Mar 2016


  • copulas-Hilbert

    copulas_Hilbert_rev.pdf, 299 KB, application/pdf

    Uploaded date:05 Apr 2016

    Version:Accepted author manuscript

King's Authors


In this article, the concept of copulas is generalised to infinite dimensional Hilbert spaces. We show one direction of Sklar’s theorem and explain that the other direction fails in infinite dimensional Hilbert spaces. We derive a necessary and sufficient condition which allows to state this direction of Sklar’s theorem in Hilbert spaces. We consider copulas with densities and specifically construct copulas in a Hilbert space by a family of pairwise copulas with densities.

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