Characterization of dependence of multidimensional Levy processes using. Levy copulas

This paper suggests Levy copulas in order to characterize the dependence among components of multidimensional Levy processes. This concept parallels the notion of a copula on the level of Levy measures. As for random vectors, a version of Sklar's theorem states that the law of a general multivariate Levy process is obtained by combining arbitrary univariate Levy processes with an arbitrary Levy copula. We construct parametric families of Levy copulas and prove a limit theorem, which indicates how to obtain the Levy copula of a multivariate Levy process X from the ordinary copula of the random vector X-t for small t. (c) 2005 Elsevier Inc. All rights reserved.