Free extreme values

Gerard Ben Arous; Dan Virgil Voiculescu

doi:10.1214/009117906000000016

Free extreme values

Gerard Ben Arous, Dan Virgil Voiculescu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Free probability analogs of the basics of extreme-value theory are obtained, based on Ando's spectral order. This includes classification of freely max-stable laws and their domains of attraction, using "free extremal convolutions" on the distributions. These laws coincide with the limit laws in the classical peaks-over-threshold approach. A free extremal projection-valued process over a measure-space is constructed, which is related to the free Poisson point process.

Original language	English (US)
Pages (from-to)	2037-2059
Number of pages	23
Journal	Annals of Probability
Volume	34
Issue number	5
DOIs	https://doi.org/10.1214/009117906000000016
State	Published - Sep 2006

Keywords

Ando spectral order
Free extremal process
Free max-stable laws
Generalized Pareto laws

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/009117906000000016

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AB - Free probability analogs of the basics of extreme-value theory are obtained, based on Ando's spectral order. This includes classification of freely max-stable laws and their domains of attraction, using "free extremal convolutions" on the distributions. These laws coincide with the limit laws in the classical peaks-over-threshold approach. A free extremal projection-valued process over a measure-space is constructed, which is related to the free Poisson point process.

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KW - Free max-stable laws

KW - Generalized Pareto laws

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Free extreme values

Abstract

Keywords

ASJC Scopus subject areas

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