Copula Measures and Sklar's Theorem in Arbitrary Dimensions

Autor:	Benth, Fred Espen, Di Nunno, Giulia, Schroers, Dennis
Rok vydání:	2020
Předmět:	Mathematics - Probability Mathematics - Statistics Theory 60G07 (Primary) 62H05 (Secondary) G.3
Druh dokumentu:	Working Paper
Popis:	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. Comment: 29 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.11530 Zobrazit plný text záznamu View this record from Arxiv