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On the tails of the distribution of the maximum of a smooth stationaryGaussian process

Published online by Cambridge University Press:  15 November 2002

Jean-Marc Azaïs ,
Jean-Marc Bardet  and
Mario Wschebor
Jean-Marc Azaïs
Affiliation:
Laboratoire de Statistique et de Probabilités, UMR 5583 du CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, [email protected].
Jean-Marc Bardet
Affiliation:
Laboratoire de Statistique et de Probabilit és, UMR 5583 du CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulou se Cedex 4, [email protected].
Mario Wschebor
Affiliation:
Centro de Matemática, Facultad de Ciencias, Universidad de la República, Calle Iguá , Montevideo, Uruguay; [email protected].
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Abstract

We study the tails of the distribution of the maximum of a stationaryGaussian process on a bounded interval of the real line. Under regularityconditions 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 [CITE] for a sufficiently small interval.

Keywords

Tail of distribution of the maximumstationary Gaussianprocesses.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 6: New directions in Time Series Analysis (Guest Editor: Philippe Soulier)New directions in Time Series Analysis (Guest Editor: Philippe Soulier) , 2002 , pp. 177 - 184
Copyright
© EDP Sciences, SMAI, 2002

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References

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