| Issue |
ESAIM: PS
Volume 6, 2002
|
|
|---|---|---|
| Page(s) | 177 - 184 | |
| DOI | https://doi.org/10.1051/ps:2002010 | |
| Published online | 15 November 2002 | |
On the tails of the distribution of the maximum of a smooth stationary Gaussian process
1
Laboratoire de Statistique et de Probabilités, UMR
5583 du CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France.azais@cict.fr.
2
Laboratoire de Statistique et de Probabilit
és, UMR
5583 du CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulou
se Cedex 4, France.bardet@cict.fr.
3
Centro de Matemática, Facultad de Ciencias, Universidad de la
República, Calle Iguá , Montevideo, Uruguay;
wscheb@fcien.edu.uy.
Received:
13
March
2002
Revised:
15
May
2002
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 [CITE] for a sufficiently small interval.
Mathematics Subject Classification: 60Gxx / 60E05 / 60G15 / 65U05
Key words: Tail of distribution of the maximum / stationary Gaussian processes.
© EDP Sciences, SMAI, 2002
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