Copulas and complex analysis: Holomorphic extensions, rigidity and regularity

Rachid Jaafar; Ahmed Hfa; Mohamed Elmaazouz; Rachid Jaafar; Ahmed Hfa; Mohamed Elmaazouz

doi:10.3934/math.20261264

AIMS Mathematics

2026, Volume 11, Issue 9: 32159-32180. doi: 10.3934/math.20261264

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Research article

Copulas and complex analysis: Holomorphic extensions, rigidity and regularity

1.
Systems Engineering and Information Technology Laboratory (LISTI), Department of Mathematics, National School of Applied Sciences (ENSA), Ibn Zohr University, Agadir, Morocco
2.
Mathematics and Applications to Engineering Sciences Laboratory (MASI), Department of Mathematics, Higher Normal School (ENS), Sidi Mohamed Ben Abdellah University, Fes, Morocco
3.
Mathematical Analysis and Applications Laboratory (LAMA), Department of Mathematics, Regional Centre for Education and Training Professions (CRMEF), Inezgane, Morocco

Received: 05 July 2026 Revised: 16 September 2026 Accepted: 21 September 2026 Published: 29 September 2026
MSC : 31A05, 32A10, 32D20, 35J25, 62H05

The rigidity of holomorphic functions leads us, after exploring the harmonic aspect of the copulas in our previous work, to the possibility of making them more flexible to better suit analytical treatment. This requires making concessions on the boundary conditions and exploring the price to be paid in terms of the loss of stochastic information. Two ways to address the complexification procedure are developed.
- complex analysis,
- copulas,
- Hartogs' theorem,
- Dirichlet problem,
- regularity
Citation: Rachid Jaafar, Ahmed Hfa, Mohamed Elmaazouz. Copulas and complex analysis: Holomorphic extensions, rigidity and regularity[J]. AIMS Mathematics, 2026, 11(9): 32159-32180. doi: 10.3934/math.20261264

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Abstract

The rigidity of holomorphic functions leads us, after exploring the harmonic aspect of the copulas in our previous work, to the possibility of making them more flexible to better suit analytical treatment. This requires making concessions on the boundary conditions and exploring the price to be paid in terms of the loss of stochastic information. Two ways to address the complexification procedure are developed.

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