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Pré-Publication, Document De Travail Année : 2014

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.
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Dates et versions

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

Identifiants

  • HAL Id : hal-01102343 , version 1

Citer

Céline Lacaux, Gennady Samorodnitsky. Time-changed Extremal Process as a Random Sup Measure. 2014. ⟨hal-01102343v1⟩
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