Lévy copulas: dynamics and transforms of Upsilon-type
نویسندگان
چکیده
Lévy processes and infinitely divisible distributions are increasingly defined in terms of their Lévy measure. In order to describe the dependence structure of a multivariate Lévy measure, Tankov (2003) introduced positive Lévy copulas. Together with the marginal Lévy measures they completely describe multivariate Lévy measures on R+ . In this paper, we show that any such Lévy copula defines itself a Lévy measure with 1-stable margins, in a canonical way. A limit theorem is obtained, characterising convergence of Lévy measures with the aid of Lévy copulas. Homogeneous Lévy copulas are considered in detail. They correspond to Lévy processes which have a time-constant Lévy copula, and a complete description of homogeneous Lévy copulas is obtained. A general sheme to construct multivariate distributions having special properties is outlined, for distributions with prescribed margins having the same properties. This makes use of Lévy copulas and of certain mappings of Upsilon type. The construction is then exemplified for distributions in the Goldie-Steutel-Bondesson class, the Thorin class and for selfdecomposable distributions. ∗Department of Mathematical Sciences, University of Aarhus, Ny Munkgade, DK-8000 Aarhus C, Denmark, email: [email protected] †Centre for Mathematical Sciences, Munich University of Technology, Boltzmannstraße 3, D-85747 Garching, Germany, email: [email protected]
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تاریخ انتشار 2005