On bivariate Archimedean copulas with fractal support

Sánchez Juan Fernández () and Trutschnig Wolfgang ()
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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

Dependence Modeling, 2025, vol. 13, issue 1, 13

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 .

Keywords: copula; doubly stochastic measure; fractal; singular function; Markov kernel (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:13:y:2025:i:1:p:13:n:1001

DOI: 10.1515/demo-2025-0013

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