Rare-event simulation and efficient discretization for the supremum of Gaussian random fields. (September 2015)

• Record Type: Journal Article
• Authors: Li, Xiaoou; Liu, Jingchen
• Is Part Of: Advances in applied probability. Volume 47:Number 3(2015)
• Page Start: 787
• Page End: 816
• Publication Date: 2015-09
• Subjects: Gaussian random field, -- high-level excursion, -- Monte Carlo, -- tail distribution, -- efficiency; 60G15, -- 65C05, -- 60G60, -- 62G32; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1239/aap/1444308882
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract : 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 probabilitiesℙ {sup T f ( 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.