Abstract
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 Darsow, Nguyen, and Olsen 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.
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© 1997 Springer Science+Business Media Dordrecht
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Li, X., Mikusiński, P., Sherwood, H., Taylor, M.D. (1997). On Approximation of Copulas. In: Beneš, V., Štěpán, J. (eds) Distributions with given Marginals and Moment Problems. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5532-8_13
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DOI: https://doi.org/10.1007/978-94-011-5532-8_13
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