Functional analysis of multivariate max-stable distributions

2025/09/02 by Costacèque-Cecchi, Bruno, Decreusefond, Laurent
#FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2509.02200

Abstract

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.

Citations

• Convergence rate for the coupon collector's problem with Stein's method
• Non-integrable stable approximation by Stein's method
• Approximation of stable law in Wasserstein-1 distance by Stein's method
• The Stein-Dirichlet-Malliavin method
• Normal approximation on Poisson spaces: Mehler's formula, second order\n Poincar 'e inequalities and stabilization
• Rates of convergence towards the Fréchet distribution
• Strictly stable distributions on convex cones

Cited by

• Stein's method for max-stable random vectors

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