Double extreme on joint sets for Gaussian random fields

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1 Scopus citations

Abstract

For a centered Gaussian random field X={X(t),t∈RN}, let T1 and T2 be two compact sets in RN such that I = T1T2 ≠ 0{combining long solidus overlay} and denote by χ (A u (I) ) the Euler characteristic of the excursion set A u (I) = {t ∈ I: X (t) ≥ u} We show that under certain smoothness and regularity conditions, as u → ∞, the joint excursion probability P{supt∈T1X(t)≥u,sups∈T2X(s)≥u} can be approximated by the expected Euler characteristic E{χ(Au(I))} such that the error is super-exponentially small.

Original languageEnglish (US)
Pages (from-to)79-82
Number of pages4
JournalStatistics and Probability Letters
Volume92
DOIs
StatePublished - Sep 2014
Externally publishedYes

Keywords

  • Euler characteristic
  • Excursion probability
  • Excursion set
  • Gaussian random fields

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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