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Semicopulas: characterizations and applicability

Fabrizio Durante;  José Quesada-Molina;  Carlo Sempi — 2006

Kybernetika

We characterize some bivariate semicopulas and, among them, the semicopulas satisfying a Lipschitz condition. In particular, the characterization of harmonic semicopulas allows us to introduce a new concept of depedence between two random variables. The notion of multivariate semicopula is given and two applications in the theory of fuzzy measures and stochastic processes are given.

Remarks on Two Product-like Constructions for Copulas

Fabrizio Durante;  Erich Peter Klement;  José Quesada-Molina;  Peter Sarkoci — 2007

Kybernetika

We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the * -product and the ☆ -product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.

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