Efficient Simulation for Tail Probabilities of Gaussian Random Field Extrema
نویسندگان
چکیده
We are interested in computing tail probabilities for the maxima of smooth 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 KarhunenLoève expansions. For the 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. In the second case we propose an estimator which is asymptotically efficient. These results serve as the first step analysis of the rare-event simulation for smooth Gaussian random fields.
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