Copula Measures and Sklar's Theorem in Arbitrary Dimensions

Fred Espen Benth; Giulia Di Nunno; Dennis Schroers

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arXiv · 2012.11530

Copula Measures and Sklar's Theorem in Arbitrary Dimensions

Fred Espen Benth·Giulia Di Nunno·Dennis Schroers

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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.

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BibTeX RIS

Fred Espen Benth, Giulia Di Nunno, Dennis Schroers. 2020-12-21. Copula Measures and Sklar's Theorem in Arbitrary Dimensions. https://arxiv.org/abs/2012.11530

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