Computation of the distribution of the maximum of stationary Gaussian sequences and processes

Jean-Marc Azaïs

Université de Toulouse, France

We first present MCQMC (Monte-Carlo Quasi Monte-Carlo) methods for computing high dimension Gaussian integrals. Then we introduce upper- and lower- bounds for the distribution of the maximum of random sequences and process by discretization or by the Record method that look at the first time the process crosses a given level. High dimensional Gaussian integration permits to compute these bounds and we present several numerical applications to practical cases.