A scalar product for copulas

被引：16

作者：

Siburg, Karl Friedrich ^{[1
]}

Stoimenov, Pavel A. ^{[2
]}

机构：

[1] Tech Univ, Fak Math, D-44227 Dortmund, Germany

[2] Tech Univ, Fak Stat, D-44227 Dortmund, Germany

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 344卷 / 01期

关键词：

copula; scalar product; Sobolev space;

D O I：

10.1016/j.jmaa.2008.02.045

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：429 / 439

页数：11

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