Asymptotic expansions for the distribution of the maximum of Gaussian random fields

Some asymptotic results are proved for the distribution of the maximum of a centered Gaussian random field with unit variance on a compact subset S of R^N. They are obtained by a Rice method and the evaluation of some moments of the number of local maxima of the Gaussian field above an high level in...

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Bibliographic Details
Published in:Extremes (Boston) 2002-06, Vol.5 (2), p.181-212
Main Authors: AZAÏS, Jean-Marc, DELMAS, Céline
Format: Article
Language:English
Subjects:
Distribution theory
Exact sciences and technology
Inference from stochastic processes
time series analysis
Life Sciences
Linear inference, regression
Mathematics
Normal distribution
Probability and statistics
Probability theory and stochastic processes
Random variables
Sciences and techniques of general use
Statistical methods
Statistics
Stochastic processes
Studies
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Summary:Some asymptotic results are proved for the distribution of the maximum of a centered Gaussian random field with unit variance on a compact subset S of R^N. They are obtained by a Rice method and the evaluation of some moments of the number of local maxima of the Gaussian field above an high level inside S and on the border partial differential of S. Depending on the geometry of the border we give up to N+1 terms of the expansion sometimes with exponentially small remainder. Application to waves maximum is shown. [PUBLICATION ABSTRACT]
ISSN:1386-1999
1572-915X