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

Xiaoou Li, Jingchen Liu

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

In this paperweconsider 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{supT 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.

Original languageEnglish (US)
Pages (from-to)787-816
Number of pages30
JournalAdvances in Applied Probability
Volume47
Issue number3
DOIs
StatePublished - Sep 2015

Keywords

  • Efficiency
  • Gaussian random field
  • High-level excursion
  • Monte Carlo
  • Tail distribution

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