Excursion probability of certain non-centered smooth Gaussian random fields

Research output: Contribution to journalArticle

Abstract

Let X={X(t),t∈T} be a non-centered, unit-variance, smooth Gaussian random field indexed on some parameter space T, and let Au(X,T)={t∈T:X(t)≥u} be the excursion set. It is shown that, as u→∞, the excursion probability ℙ{supt∈TX(t)≥u} can be approximated by the expected Euler characteristic of Au(X,T), denoted by E{χ(Au(X,T))}, such that the error is super-exponentially small. The explicit formulae for E{χ(Au(X,T))} are also derived for two cases: (i) T is a rectangle and X-EX is stationary; (ii) T is an N-dimensional sphere and X-EX is isotropic.

Original languageEnglish (US)
Pages (from-to)883-905
Number of pages23
JournalStochastic Processes and their Applications
Volume126
Issue number3
DOIs
StatePublished - Mar 2016

Keywords

  • Euler characteristic
  • Excursion probability
  • Gaussian random fields
  • Rectangle
  • Sphere
  • Super-exponentially small

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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