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On approximation of copulas. (English) Zbl 0905.60015

Beneš, Viktor (ed.) et al., Distributions with given marginals and moment problems. Proceedings of the 1996 conference, Prague, Czech Republic. Dordrecht: Kluwer Academic Publishers. 107-116 (1997).
Summary: One can hope to prove interesting properties of copulas by verifying them first for some class of “simple” copulas then invoking a limit process. The most commonly used limit for copulas is the uniform limit. However the uniform limit is not completely satisfactory in that, on the one hand, any copula can be approximated arbitrarily closely by invertible copulas and, on the other hand, the \(*\) operation of W. F. Darsow, B. Nguyen, and E. T. Olsen [Ill. J. Math. 36, No. 4, 600-642 (1992; Zbl 0770.60019)] is not jointly continuous with respect to the uniform limit. We show that certain approximations of copulas lead naturally to a stronger convergence than uniform convergence and give a short proof of the associativity of \(*\) as an application.
For the entire collection see [Zbl 0885.00054].

MSC:

60E99 Distribution theory

Citations:

Zbl 0770.60019
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