Functional analysis of multivariate max-stable distributions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912566596337664 |
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| author | Costacèque-Cecchi, Bruno Decreusefond, Laurent |
| author_facet | Costacèque-Cecchi, Bruno Decreusefond, Laurent |
| contents | We study the connections existing between max-infinitely divisible distributions and Poisson processes from the point of view of functional analysis. More precisely, we derive functional identities for the former by using well-known results of Poisson stochastic analysis. We also introduce a family of Markov semigroups whose stationary measures are the so-called multivariate max-stable distributions. Their generators thus provide a functional characterization of extreme valued distributions in any dimension. Additionally, we give a few functional identities associated to those semi-groups, namely a Poincar{é} identity and commutation relations. Finally, we present a stochastic process whose semigroup corresponds to the one we introduced and that can be expressed using extremal stochastic integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02200 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional analysis of multivariate max-stable distributions Costacèque-Cecchi, Bruno Decreusefond, Laurent Functional Analysis Probability We study the connections existing between max-infinitely divisible distributions and Poisson processes from the point of view of functional analysis. More precisely, we derive functional identities for the former by using well-known results of Poisson stochastic analysis. We also introduce a family of Markov semigroups whose stationary measures are the so-called multivariate max-stable distributions. Their generators thus provide a functional characterization of extreme valued distributions in any dimension. Additionally, we give a few functional identities associated to those semi-groups, namely a Poincar{é} identity and commutation relations. Finally, we present a stochastic process whose semigroup corresponds to the one we introduced and that can be expressed using extremal stochastic integrals. |
| title | Functional analysis of multivariate max-stable distributions |
| topic | Functional Analysis Probability |
| url | https://arxiv.org/abs/2509.02200 |