Computing the Distribution of the Maximum of Gaussian Random Processes

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.