Stochastic modelling in physical oceanography
Stochastic modelling in physical oceanography
Fast simulation of overflow probabilities in a queue with Gaussian input
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Rare-event simulations for exponential integrals of smooth Gaussian processes
Proceedings of the Winter Simulation Conference
Monte Carlo for large credit portfolios with potentially high correlations
Proceedings of the Winter Simulation Conference
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We are interested in computing tail probabilities for the maxima of Gaussian random fields. In this paper, we discuss two special cases: random fields defined over a finite number of distinct point and fields with finite Karhunen-Loève expansions. For the first case we propose an importance sampling estimator which yields asymptotically zero relative error. Moreover, it yields a procedure for sampling the field conditional on it having an excursion above a high level with a complexity that is uniformly bounded as the level increases. In the second case we propose an estimator which is asymptotically optimal. These results serve as a first step analysis of rare-event simulation for Gaussian random fields.