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

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

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.

Original language	English
Pages (from-to)	177-184
Number of pages	8
Journal	ESAIM - Probability and Statistics
Volume	6
DOIs	https://doi.org/10.1051/ps:2002010
Publication status	Published - 1 Dec 2002
Externally published	Yes

Keywords

Stationary Gaussian processes
Tail of distribution of the maximum

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10.1051/ps:2002010

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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 - Bardet, Jean Marc

AU - Wschebor, Mario

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N2 - 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.

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.

KW - Stationary Gaussian processes

KW - Tail of distribution of the maximum

U2 - 10.1051/ps:2002010

DO - 10.1051/ps:2002010

M3 - Article

AN - SCOPUS:0037002678

SN - 1292-8100

VL - 6

SP - 177

EP - 184

JO - ESAIM - Probability and Statistics

JF - ESAIM - Probability and Statistics

ER -

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

Abstract

Keywords

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