Copula Measures and Sklar's Theorem in Arbitrary Dimensions
Probability
2020-12-23 v2 Statistics Theory
Statistics Theory
Abstract
Although copulas are used and defined for various infinite-dimensional objects (e.g. Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified approach and define copulas as probability measures on general product spaces. For this we prove Sklar's Theorem in this infinite-dimensional setting. We show how to transfer this result to various function space settings and describe how to model and approximate dependent probability measures in these spaces in the realm of copulas.
Cite
@article{arxiv.2012.11530,
title = {Copula Measures and Sklar's Theorem in Arbitrary Dimensions},
author = {Fred Espen Benth and Giulia Di Nunno and Dennis Schroers},
journal= {arXiv preprint arXiv:2012.11530},
year = {2020}
}
Comments
29 pages