Computing the distribution of the maximum of Gaussian random processes

Christine Cierco-Ayrolles (1) , Alain Croquette (2) , Céline Delmas (3)

1 UBIA - Unité de Biométrie et Intelligence Artificielle (ancêtre de MIAT)
2 UT3 - Université Toulouse III - Paul Sabatier
3 SGQA - Station de Génétique Quantitative et Appliquée

The aim of this paper is to propose an Splus program to calculate bounds for the distribution of the maximum of a smooth Gaussian process on a fixed interval. We generalize the results given in Azaïs et al. (1999) to the case of the absolute value of the Gaussian process and to the non-homogeneous case. Our method relies on calculations of the first three terms of the Rice's series. Some applications are given to illustrate the method and the performances of the program. The corresponding Splus functions are available at the URL: http://www.lsp.ups-tlse.fr/Cdelmas/software.html.

Domaines: Sciences du Vivant [q-bio]

Christine Cierco-Ayrolles, Alain Croquette, Céline Delmas. Computing the distribution of the maximum of Gaussian random processes. Methodology and Computing in Applied Probability, 2003, 5, pp.427-438. ⟨10.1023/A:1026233412905⟩. ⟨hal-02678872⟩