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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 [11] for a sufficiently small interval.
@article{PS_2002__6__177_0,
author = {Aza{\"\i}s, Jean-Marc and Bardet, Jean-Marc and Wschebor, Mario},
title = {On the tails of the distribution of the maximum of a smooth stationary gaussian process},
journal = {ESAIM: Probability and Statistics},
pages = {177--184},
publisher = {EDP-Sciences},
volume = {6},
year = {2002},
doi = {10.1051/ps:2002010},
mrnumber = {1943146},
zbl = {1009.60022},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2002010/}
}
TY - JOUR AU - Azaïs, Jean-Marc AU - Bardet, Jean-Marc AU - Wschebor, Mario TI - On the tails of the distribution of the maximum of a smooth stationary gaussian process JO - ESAIM: Probability and Statistics PY - 2002 SP - 177 EP - 184 VL - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps:2002010/ DO - 10.1051/ps:2002010 LA - en ID - PS_2002__6__177_0 ER -
%0 Journal Article %A Azaïs, Jean-Marc %A Bardet, Jean-Marc %A Wschebor, Mario %T On the tails of the distribution of the maximum of a smooth stationary gaussian process %J ESAIM: Probability and Statistics %D 2002 %P 177-184 %V 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps:2002010/ %R 10.1051/ps:2002010 %G en %F PS_2002__6__177_0
Azaïs, Jean-Marc; Bardet, Jean-Marc; Wschebor, Mario. On the tails of the distribution of the maximum of a smooth stationary gaussian process. ESAIM: Probability and Statistics, Tome 6 (2002), pp. 177-184. doi: 10.1051/ps:2002010
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