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tail of distribution of the maximum

ESAIM: Probability and Statistics (1)

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On the tails of the distribution of the maximum of a smooth stationaryGaussian process
Jean-Marc Azaïs, Jean-Marc Bardet, Mario Wschebor
Journal:

ESAIM: Probability and Statistics / Volume 6 / 2002

Published online by Cambridge University Press:

15 November 2002, pp. 177-184

Print publication:

2002
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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.