Rare-event simulation and efficient discretization for the supremum of Gaussian random fields

Abstract

In this paper we consider a classic problem concerning the high excursion probabilities of a Gaussian random fieldfliving on a compact setT. We develop efficient computational methods for the tail probabilitiesℙ{supTf(t) >b}. For each positive ε, we present Monte Carlo algorithms that run inconstanttime and compute the probabilities with relative error ε for arbitrarily largeb. The efficiency results are applicable to a large class of Hölder continuous Gaussian random fields. Besides computations, the change of measure and its analysis techniques have several theoretical and practical indications in the asymptotic analysis of Gaussian random fields.