Baire category results for quasi–copulas

Fabrizio Durante 1 , Juan Fernández-Sánchez 2 ,  and Wolfgang Trutschnig 3
  • 1 Faculty of Economics and Management, Free University of Bozen-Bolzano, Bolzano, Italy
  • 2 Grupo de Investigación de Análisis Matemático, Universidad de Almería, La Cañada de San Urbano, Almería, Spain
  • 3 Department for Mathematics, University of Salzburg, Salzburg, Austria


The aim of this manuscript is to determine the relative size of several functions (copulas, quasi– copulas) that are commonly used in stochastic modeling. It is shown that the class of all quasi–copulas that are (locally) associated to a doubly stochastic signed measure is a set of first category in the class of all quasi– copulas. Moreover, it is proved that copulas are nowhere dense in the class of quasi-copulas. The results are obtained via a checkerboard approximation of quasi–copulas.

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Dependence Modeling aims to provide a medium for exchanging results and ideas in the area of multivariate dependence modeling. Topics include Copula methods, environmental sciences, estimation and goodness-of-fit tests, extreme-value theory, limit laws, mass transportations, measures of association, multivariate distributions and tests, quantitative risk management, risk assessment, risk models, risk measures and stochastic orders and time series.