Double extreme on joint sets for Gaussian random fields

Research output: Contribution to journalArticle

1 Citation (Scopus)

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

Fingerprint

Gaussian Random Field
Excursion
Euler Characteristic
Extremes
Regularity Conditions
Overlay
Compact Set
Smoothness
Denote
Random field
Regularity

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Double extreme on joint sets for Gaussian random fields. / Cheng, Dan.

In: Statistics and Probability Letters, Vol. 92, 09.2014, p. 79-82.

Research output: Contribution to journalArticle

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