L�vy Copulas: Dynamics and Transforms of Upsilon Type
研究了Lévy联结函数的性质，证明其自身定义一种具有一稳定边际的Lévy测度，并得到收敛定理。详细讨论了齐次Lévy联结函数，提出构造具有特殊性质的多元分布的一般方法，适用于Goldie-Steutel-Bondesson类、Thorin类和自可分解分布。
Abstract. 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 Lévy copulas on . (For an extension to ℝm, see Kallsen & Tankov, 2006.) Together with the marginal Lévy measures they completely describe multivariate Lévy measures on . In this article we show that any such Lévy copula defines itself a Lévy measure with one-stable margins, in a canonical way. A limit theorem is obtained, characterizing 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 scheme 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 self-decomposable distributions.