On the tails of the distribution of the maximum of a smooth stationary Gaussian process

Jean Marc Azaïs; Jean Marc Bardet; Mario Wschebor

doi:10.1051/ps:2002010

On the tails of the distribution of the maximum of a smooth stationary Gaussian process

Jean Marc Azaïs
, Jean Marc Bardet
, Mario Wschebor

Université de Toulouse
Universidad de la República

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We study the tails of the distribution of the maximum of a stationary Gaussian process on a bounded interval of the real line. Under regularity conditions including the existence of the spectral moment of order 8, we give an additional term for this asymptotics. This widens the application of an expansion given originally by Piterbarg for a sufficiently small interval.

langue originale	Anglais
Pages (de - à)	177-184
Nombre de pages	8
journal	ESAIM - Probability and Statistics
Volume	6
Les DOIs	https://doi.org/10.1051/ps:2002010
état	Publié - 1 déc. 2002
Modification externe	Oui

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10.1051/ps:2002010

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title = "On the tails of the distribution of the maximum of a smooth stationary Gaussian process",

abstract = "We study the tails of the distribution of the maximum of a stationary Gaussian process on a bounded interval of the real line. Under regularity conditions including the existence of the spectral moment of order 8, we give an additional term for this asymptotics. This widens the application of an expansion given originally by Piterbarg for a sufficiently small interval.",

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AU - Wschebor, Mario

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AB - We study the tails of the distribution of the maximum of a stationary Gaussian process on a bounded interval of the real line. Under regularity conditions including the existence of the spectral moment of order 8, we give an additional term for this asymptotics. This widens the application of an expansion given originally by Piterbarg for a sufficiently small interval.

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DO - 10.1051/ps:2002010

M3 - Article

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JO - ESAIM - Probability and Statistics

JF - ESAIM - Probability and Statistics

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On the tails of the distribution of the maximum of a smooth stationary Gaussian process

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