Geodesic
n-dimensional copulas and weak derivatives
Serdica Mathematical Journal, Tome 44 (2018) no. 3-4, pp. 413-438.

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In the copula theory universe the number of multivariate copulas is very limited. This is caused by both of non-trivial tasks - to check the n-increasing property and to define the copula. We generalize the notion of n-increasing property in terms of weak derivatives which allows us to simplify the otherwise complex former method. Furthermore, we demonstrate the applicability of our approach to the class of n-dimensional Archimedean copulas. Finally, we present a method which allows us to obtain a class of copulas as a solution of a boundary value problem in appropriate Sobolev spaces.
Keywords: copula, n-increasing function, weak solution, test function, 35L05, 35L20, 46FXX, 46F10, 46F12, 60E05, 62F99 
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     title = {n-dimensional copulas and weak derivatives},
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Chervenov, Nikolay; Iordanov, Iordan; , Kostadinov, Boyan. n-dimensional copulas and weak derivatives. Serdica Mathematical Journal, Tome 44 (2018) no. 3-4, pp. 413-438. http://geodesic.mathdoc.fr/item/SMJ2_2018_44_3-4_a5/