The Tail of the Maximum of Smooth Gaussian Fields on Fractal Sets

Jean-Marc Azaïs () and Mario Wschebor ()
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Jean-Marc Azaïs: Université Paul Sabatier
Mario Wschebor: Universidad de la República

Journal of Theoretical Probability, 2014, vol. 27, issue 3, 932-944

Abstract: Abstract We study the probability distribution of the maximum M S of a smooth stationary Gaussian field defined on a fractal subset S of ℝ n . Our main result is the equivalent of the asymptotic behavior of the tail of the distribution ℙ(M S >u) as u→+∞. The basic tool is the Rice formula for the moments of the number of local maxima of a random field.

Keywords: Gaussian fields; Rice formula; Distribution of the maximum; Maximum on fractals; Self-similar sets; Minkowski measurable sets; 60G15; 60G70 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-012-0429-0

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