Asymptotic Expansions for the Distribution of the Maximum of Gaussian Random Fields

Authors: AZAÏS, J-M.¹; Delmas, C.²

Source: Extremes, Volume 5, Number 2, June 2002 , pp. 181-212(32)

Publisher: Springer

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Abstract:

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 ∂ 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.

Keywords: asymptotic expansions; Gaussian fields; maxima of random fields; rice method

Document Type: Research article

Affiliations: 1: Laboratoire de Statistique et Probabilités, UMR CNRS C5583 Université Paul-Sabatier, 31062 Toulouse, France azais@cict.fr 2: Laboratoire de Statistique et Probabilités, UMR CNRS C5583 Université Paul-Sabatier, 31062 Toulouse, France cdelmas@cict.fr

Publication date: 2002-06-01