Efficient simulations for the exponential integrals of Hölder continuous gaussian random fields

Abstract

In this article, we consider a Gaussian random field f ( t ) living on a compact set T ⊂ R d and the computation of the tail probabilities P (∫ T e f ( t ) dt > e b ) as b → ∞. We design asymptotically efficient importance sampling estimators for a general class of Hölder continuous Gaussian random fields. In addition to the variance control, we also analyze the bias (relative to the interesting tail probabilities) caused by the discretization.