Advances in Applied Probability

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

Xiaoou Li and Jingchen Liu

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In this paper we consider a classic problem concerning the high excursion probabilities of a Gaussian random field f living on a compact set T. We develop efficient computational methods for the tail probabilities P{supTf(t) > b}. For each positive ε, we present Monte Carlo algorithms that run in constant time and compute the probabilities with relative error ε for arbitrarily large b. 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.

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Adv. in Appl. Probab., Volume 47, Number 3 (2015), 787-816.

First available in Project Euclid: 8 October 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G15: Gaussian processes 65C05: Monte Carlo methods
Secondary: 60G60: Random fields 62G32: Statistics of extreme values; tail inference

Gaussian random field high-level excursion Monte Carlo tail distribution efficiency


Li, Xiaoou; Liu, Jingchen. Rare-event simulation and efficient discretization for the supremum of Gaussian random fields. Adv. in Appl. Probab. 47 (2015), no. 3, 787--816. doi:10.1239/aap/1444308882.

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