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

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 > eb) 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.