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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| Format: | Article |
| Language: | English |
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De Gruyter
2025-05-01
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| Series: | Dependence Modeling |
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| Online Access: | https://doi.org/10.1515/demo-2025-0013 |
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| _version_ | 1850132547067969536 |
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| author | Sánchez Juan Fernández Trutschnig Wolfgang |
| author_facet | Sánchez Juan Fernández Trutschnig Wolfgang |
| author_sort | Sánchez Juan Fernández |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f932a2de9bec453fb57f8dfb2a0e7afa |
| institution | OA Journals |
| issn | 2300-2298 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Dependence Modeling |
| spelling | doaj-art-f932a2de9bec453fb57f8dfb2a0e7afa2025-08-20T02:32:11ZengDe GruyterDependence Modeling2300-22982025-05-0113143145010.1515/demo-2025-0013On bivariate Archimedean copulas with fractal supportSánchez Juan Fernández0Trutschnig Wolfgang1Grupo de Investigación de Análisis Matemático, Universidad de Almería, La Cannnada de San Urbano, 04120, Almería, SpainDepartment for Artificial Intelligence & Human Interfaces, University of Salzburg, Hellbrunnerstrasse 34, 5020 Salzburg, AustriaDue 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.https://doi.org/10.1515/demo-2025-0013copuladoubly stochastic measurefractalsingular functionmarkov kernel62h2060e0528a8026a30 |
| spellingShingle | Sánchez Juan Fernández Trutschnig Wolfgang On bivariate Archimedean copulas with fractal support Dependence Modeling copula doubly stochastic measure fractal singular function markov kernel 62h20 60e05 28a80 26a30 |
| title | On bivariate Archimedean copulas with fractal support |
| title_full | On bivariate Archimedean copulas with fractal support |
| title_fullStr | On bivariate Archimedean copulas with fractal support |
| title_full_unstemmed | On bivariate Archimedean copulas with fractal support |
| title_short | On bivariate Archimedean copulas with fractal support |
| title_sort | on bivariate archimedean copulas with fractal support |
| topic | copula doubly stochastic measure fractal singular function markov kernel 62h20 60e05 28a80 26a30 |
| url | https://doi.org/10.1515/demo-2025-0013 |
| work_keys_str_mv | AT sanchezjuanfernandez onbivariatearchimedeancopulaswithfractalsupport AT trutschnigwolfgang onbivariatearchimedeancopulaswithfractalsupport |