Time-changed extremal process as a random sup measure - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bernoulli Année : 2016

Time-changed extremal process as a random sup measure

Résumé

A functional limit theorem for the partial maxima of a long memory stable sequence produces a limiting process that can be described as a β-power time change in the classical Fréchet extremal process, for β in a subinterval of the unit interval. Any such power time change in the extremal process for 0 < β < 1 produces a process with stationary max-increments. This deceptively simple time change hides the much more delicate structure of the resulting process as a self-affine random sup measure. We uncover this structure and show that in a certain range of the parameters this random measure arises as a limit of the partial maxima of the same long memory stable sequence, but in a different space. These results open a way to construct a whole new class of self-similar Fréchet processes with stationary max-increments.
Fichier principal
Vignette du fichier
supmeasure-rev.pdf (212.35 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01102343 , version 1 (12-01-2015)
hal-01102343 , version 2 (15-12-2015)

Identifiants

Citer

Céline Lacaux, Gennady Samorodnitsky. Time-changed extremal process as a random sup measure. Bernoulli, 2016, 22 (4), pp.1979-2000. ⟨10.3150/15-BEJ717⟩. ⟨hal-01102343v2⟩
149 Consultations
203 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More