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Włodzimierz Wysocki
Characterizations of multivariate Archimedean quasi-copulas
978
Abstract
In this paper we discuss three new characterizations of
n-dimensional Archimedean quasi-copulas. The first (differential)
characterization is a generalization of the analogous fact for
2-dimensional Archimedean copulas. The second (asymptotic)
characterization concerns a representation of Archimedean quasi-copulas
as the limit of an almost uniformly convergent sequence of functions
which depend on multiple superpositions of diagonal sections.
The last (vector) characterization makes use of the form of the projection
of an Archimedean 2-copula which uniquely determines its vector generator.
The solution of some differential equation which involves this generator
gives the pseudoinverse of the additive generator of the Archimedean
n-quasi-copula.
Keywords: quasi-copula, Archimedean quasi-copula, diagonal section of a
quasi-copula, projection of a 2-copula, vector generator of an Archimedean
2-copula (Archimedean n-quasi-copula).
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