Copulae of probability measures on product spaces

Marco Scarsini (1, 2)

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 Dipartimento di Scienze Economiche e Aziendali

It has been proved (Sklar, 1959, Publ. Inst. Statist. Univ. Paris 8 229–231) that any multivariate distribution function depends on its arguments only through its marginal distributions. An analogous result will be proved in the general framework of probability measures on (Polish) product spaces. Many properties, holding for distribution functions, still hold in the more general situation. Some results related to convergence in probability will be examined.

Mots clés: copula; probability measures on product spaces; simulation of multivariate distributions; multivariate random processes; convergence in probability

Domaines: Economie et sciences de la décision

Marco Scarsini. Copulae of probability measures on product spaces. Journal of Multivariate Analysis, 1989, Vol. 31, N°2, pp. 201-219. ⟨10.1016/0047-259X(89)90062-6⟩. ⟨hal-00542233⟩