Copulas in Hilbert spaces
Probability
2015-09-24 v1
Abstract
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.
Cite
@article{arxiv.1509.06941,
title = {Copulas in Hilbert spaces},
author = {Erika Hausenblas and Markus Riedle},
journal= {arXiv preprint arXiv:1509.06941},
year = {2015}
}