Authors: Siburg, Karl F.
Stoimenov, Pavel A.
Title: A scalar product for copulas
Language (ISO): en
Abstract: We introduce a scalar product for n-dimensional copulas, based on the Sobolev scalar product for W^1,2-functions. The corresponding norm has quite remarkable properties and provides a new, geometric framework for copulas. We show that, in the bivariate case, it measures invertibility properties of copulas with respect to the *-operation introduced by Darsow et al. (1992). The unique copula of minimal norm is the null element for the *-operation, whereas the copulas of maximal norm are precisely the invertible elements.
Subject Headings: Copula
Scalar product
Sobolev space
Issue Date: 2008-05-15T09:16:00Z
Appears in Collections:Preprints der Fakultät für Mathematik

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