On bivariate Archimedean copulas with fractal support
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 itera...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-05-01
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| Series: | Dependence Modeling |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/demo-2025-0013 |
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| Summary: | 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 As{A}_{s} fulfilling that the Hausdorff dimension of the support of As{A}_{s} is exactly ss. |
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| ISSN: | 2300-2298 |