Authors: | Siburg, Karl Friedrich 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 with respect to the ∗-product for copulas defined by Darsow et al. The unique copula of minimal norm is the null element for the ∗-multiplication, whereas the copulas of maximal norm are precisely the invertible elements. |
Subject Headings: | Copula Scalar product Sobolev space |
URI: | http://hdl.handle.net/2003/24794 http://dx.doi.org/10.17877/DE290R-15316 |
Issue Date: | 2007-10-25T11:55:28Z |
Appears in Collections: | Sonderforschungsbereich (SFB) 475 |
Files in This Item:
File | Description | Size | Format | |
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TR_32-siburg.pdf | DNB | 205.9 kB | Adobe PDF | View/Open |
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