Functional analysis of multivariate max-stable distributions
Résumé
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 Poincaré 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.
Mots clés
- 60E07
- 47D07
- max-stable distributions Math Subject Classification: 39B62
- smart path method
- generator approach
- Stein's method generator approach smart path method Mehler formula functional inequalities extreme-value theory max-stable distributions Math Subject Classification: 39B62 47D07 60E07
- extreme-value theory
- functional inequalities
- Mehler formula
- Stein's method
- Max-stable distributions
- Functional inequalities
- Stochastic quantization
| Origine | Fichiers produits par l'(les) auteur(s) |
|---|
