Free extreme values

Gerard Ben Arous, Dan Virgil Voiculescu

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)2037-2059
Number of pages23
JournalAnnals of Probability
Volume34
Issue number5
DOIs
StatePublished - Sep 2006

Fingerprint

Extreme Values
Peaks over Threshold
Free Probability
Extreme Value Theory
Poisson Point Process
Stable Laws
Limit Laws
Measure space
Domain of Attraction
Convolution
Projection
Analogue
Extreme values

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Free extreme values. / Ben Arous, Gerard; Voiculescu, Dan Virgil.

In: Annals of Probability, Vol. 34, No. 5, 09.2006, p. 2037-2059.

Research output: Contribution to journalArticle

Ben Arous, Gerard ; Voiculescu, Dan Virgil. / Free extreme values. In: Annals of Probability. 2006 ; Vol. 34, No. 5. pp. 2037-2059.
@article{0e25d30c2af346d9a1c50196f9e1b40d,
title = "Free extreme values",
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.",
keywords = "Ando spectral order, Free extremal process, Free max-stable laws, Generalized Pareto laws",
author = "{Ben Arous}, Gerard and Voiculescu, {Dan Virgil}",
year = "2006",
month = "9",
doi = "10.1214/009117906000000016",
language = "English (US)",
volume = "34",
pages = "2037--2059",
journal = "Annals of Probability",
issn = "0091-1798",
publisher = "Institute of Mathematical Statistics",
number = "5",

}

TY - JOUR

T1 - Free extreme values

AU - Ben Arous, Gerard

AU - Voiculescu, Dan Virgil

PY - 2006/9

Y1 - 2006/9

N2 - 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.

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.

KW - Ando spectral order

KW - Free extremal process

KW - Free max-stable laws

KW - Generalized Pareto laws

UR - http://www.scopus.com/inward/record.url?scp=33845505094&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845505094&partnerID=8YFLogxK

U2 - 10.1214/009117906000000016

DO - 10.1214/009117906000000016

M3 - Article

VL - 34

SP - 2037

EP - 2059

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 5

ER -