Copulas in Hilbert spaces
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in: Stochastics, Jahrgang 89.2017, Nr. 1, 16.03.2016, S. 222-239.
Publikationen: Beitrag in Fachzeitschrift › Artikel › Forschung › (peer-reviewed)
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TY - JOUR
T1 - Copulas in Hilbert spaces
AU - Hausenblas, Erika
AU - Markua, Riedle
PY - 2016/3/16
Y1 - 2016/3/16
N2 - 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.
AB - 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.
U2 - 10.1080/17442508.2016.1158821
DO - 10.1080/17442508.2016.1158821
M3 - Article
VL - 89.2017
SP - 222
EP - 239
JO - Stochastics
JF - Stochastics
SN - 1744-2508
IS - 1
ER -
