On the tails of the distribution of the maximum of a smooth stationary gaussian process
ESAIM: Probability and Statistics, Volume 6 (2002), pp. 177-184.

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.

DOI: 10.1051/ps:2002010
Classification: 60Gxx,  60E05,  60G15,  65U05
Keywords: tail of distribution of the maximum, stationary gaussian processes
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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, Volume 6 (2002), pp. 177-184. doi : 10.1051/ps:2002010. http://www.numdam.org/articles/10.1051/ps:2002010/

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