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Characterization of dependence of multidimensional Lévy processes using Lévy copulas

Jan Kallsen and Peter Tankov

Journal of Multivariate Analysis, 2006, vol. 97, issue 7, 1551-1572

Abstract: This paper suggests Lévy copulas in order to characterize the dependence among components of multidimensional Lévy processes. This concept parallels the notion of a copula on the level of Lévy measures. As for random vectors, a version of Sklar's theorem states that the law of a general multivariate Lévy process is obtained by combining arbitrary univariate Lévy processes with an arbitrary Lévy copula. We construct parametric families of Lévy copulas and prove a limit theorem, which indicates how to obtain the Lévy copula of a multivariate Lévy process X from the ordinary copula of the random vector Xt for small t.

Keywords: Lévy; process; Copula; Limit; theorems (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (53)

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