Bounds and asymptotic expansions for the distribution of the maximum of a smooth stationary gaussian process
Jean-Marc Azaïs, Christine Cierco-Ayrolles, Alain Croquette (1999)
ESAIM: Probability and Statistics
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Jean-Marc Azaïs, Christine Cierco-Ayrolles, Alain Croquette (1999)
ESAIM: Probability and Statistics
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Burdzy, Krzysztof, White, David (2004)
Electronic Communications in Probability [electronic only]
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Jean-Marc Azaïs, Jean-Marc Bardet, Mario Wschebor (2010)
ESAIM: Probability and Statistics
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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 , 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.
Bel, L., Oppenheim, G., Robbiano, L., Viano, M.C. (1998)
Journal of Applied Mathematics and Stochastic Analysis
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Iglói, E., Terdik, G. (1999)
Electronic Journal of Probability [electronic only]
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Journal of Applied Mathematics and Stochastic Analysis
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Journal of Probability and Statistics
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Kybernetika
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A. Yu. Zaitsev (1998)
ESAIM: Probability and Statistics
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