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arXiv · 1109.3895

The tail of the maximum of smooth Gaussian fields on fractal sets

Jean-Marc Azaïs·Mario Wschebor
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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 $u\rightarrow +\infty.$ The basic tool is Rice formula for the moments of the number of local maxima of a random field.

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Jean-Marc Azaïs, Mario Wschebor. 2011-09-18. The tail of the maximum of smooth Gaussian fields on fractal sets. https://arxiv.org/abs/1109.3895

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