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On bivariate Archimedean copulas with fractal support

Author

Listed:
  • Sánchez Juan Fernández

    (Grupo de Investigación de Análisis Matemático, Universidad de Almería, La Cannnada de San Urbano, 04120, Almería, Spain)

  • Trutschnig Wolfgang

    (Department for Artificial Intelligence & Human Interfaces, University of Salzburg, Hellbrunnerstrasse 34, 5020 Salzburg, Austria)

Abstract

Due to their simple analytic form (bivariate) Archimedean copulas are usually viewed as very smooth and handy objects, which should distribute mass in a fairly regular and certainly not in a pathological way. Building upon recently established results on the Archimedean family and working with iterated function systems with probabilities, we falsify this natural conjecture and derive the surprising result that for every s ∈ s\hspace{0.33em}\in [1, 2] there exists some bivariate Archimedean copula A s {A}_{s} fulfilling that the Hausdorff dimension of the support of A s {A}_{s} is exactly s s .

Suggested Citation

  • Sánchez Juan Fernández & Trutschnig Wolfgang, 2025. "On bivariate Archimedean copulas with fractal support," Dependence Modeling, De Gruyter, vol. 13(1), pages 1-13.
    • Handle: RePEc:vrs:demode:v:13:y:2025:i:1:p:13:n:1001
    DOI: 10.1515/demo-2025-0013
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    References listed on IDEAS

    as
    1. Fredricks, Gregory A. & Nelsen, Roger B. & Rodriguez-Lallena, Jose Antonio, 2005. "Copulas with fractal supports," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 42-48, August.
    2. Fabrizio Durante & Juan Fernández Sánchez & Wolfgang Trutschnig, 2020. "Spatially homogeneous copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 607-626, April.
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