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Sklar’s theorem obtained via regularization techniques
Authors:Fabrizio Durante
Institution:
  • a School of Economics and Management, Free University of Bozen-Bolzano, Bolzano, Italy
  • b Grupo de Investigación de Análisis Matemático, Universidad de Almería, La Cañada de San Urbano, Almería, Spain
  • c Dipartimento di Matematica “Ennio De Giorgi”, Università del Salento, Lecce, Italy
  • Abstract:Sklar’s theorem establishes the connection between a joint d-dimensional distribution function and its univariate marginals. Its proof is straightforward when all the marginals are continuous. The hard part is the extension to the case where at least one of the marginals has a discrete component. We present a new proof of this extension based on some analytical regularization techniques (i.e., mollifiers) and on the compactness (with respect to the L norm) of the class of copulas.
    Keywords:62H05  60E05
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