Copulas in Hilbert spaces Article Swipe
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Erika Hausenblas
,
Markus Riedle
·
YOU?
·
· 2016
· Open Access
·
· DOI: https://doi.org/10.1080/17442508.2016.1158821
· OA: W2237532636
YOU?
·
· 2016
· Open Access
·
· DOI: https://doi.org/10.1080/17442508.2016.1158821
· OA: W2237532636
In this article, the concept of copulas is generalised to infinite\ndimensional Hilbert spaces. We show one direction of Sklar's theorem and\nexplain that the other direction fails in infinite dimensional Hilbert spaces.\nWe derive a necessary and sufficient condition which allows to state this\ndirection of Sklar's theorem in Hilbert spaces. We consider copulas with\ndensities and specifically construct copulas in a Hilbert space by a family of\npairwise copulas with densities.\n
Keywords: Hilbert space · Mathematics · Rigged Hilbert space · Hilbert manifold · Pure mathematics · Pairwise comparison · Reproducing kernel Hilbert space · Statistics
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