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Solution to an open problem about a transformation on the space of copulas

100%

Durante F. , Fernández-Sánchez J. , Trutschnig W.

Dependence Modeling

2014

tom 2

nr 1

We solve a recent open problem about a new transformation mapping the set of copulas into itself. The obtained mapping is characterized in algebraic terms and some limit results are proved.

Baire category results for quasi–copulas

100%

Durante F. , Fernández-Sánchez J. , Trutschnig W.

Dependence Modeling

2016

tom 4

nr 1

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.

A family of singular functions and its relation to harmonic fractal analysis and fuzzy logic

100%

de Amo E. , Carrillo M. D. , Fernández-Sánchez J.

Open Mathematics

2016

tom 14

nr 1

1039-1052

We study a parameterized family of singular functions which appears in a paper by H. Okamoto and M. Wunsch (2007). Various properties are revisited from the viewpoint of fractal geometry and probabilistic techniques. Hausdorff dimensions are calculated for several sets related to these functions, and new properties close to fractal analysis and strong negations are explored.