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Uniformly efficient simulation for extremes of Gaussian random fields

Part of: Stochastic processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  28 March 2018

Xiaoou Li  and
Gongjun Xu
Xiaoou Li*
Affiliation:
University of Minnesota
Gongjun Xu*
Affiliation:
University of Michigan
*
* Postal address: School of Statistics, University of Minnesota, 224 Church ST SE, Minneapolis, MN 55455, USA. Email address: lixx1766@umn.edu
** Postal address: Department of Statistics, University of Michigan, 1085 South University, Ann Arbor, MI 48109, USA. Email address: gongjun@umich.edu
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Abstract

In this paper we consider the problem of simultaneously estimating rare-event probabilities for a class of Gaussian random fields. A conventional rare-event simulation method is usually tailored to a specific rare event and consequently would lose estimation efficiency for different events of interest, which often results in additional computational cost in such simultaneous estimation problems. To overcome this issue, we propose a uniformly efficient estimator for a general family of Hölder continuous Gaussian random fields. We establish the asymptotic and uniform efficiency of the proposed method and also conduct simulation studies to illustrate its effectiveness.

Keywords

Rare eventimportance samplingGaussian random field

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 60G15: Gaussian processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 1 , March 2018 , pp. 157 - 178
Copyright
Copyright © Applied Probability Trust 2018 

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