Excursion probabilities of isotropic and locally isotropic Gaussian random fields on manifolds

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

Let X = {X(p), p ∈ M} be a centered Gaussian random field, where M is a smooth Riemannian manifold. For a suitable compact subset D⊂ M, we obtain approximations to the excursion probabilities ℙ { sup p DX(p) ≥ u} , as u→ ∞, for two cases: (i) X is smooth and isotropic; (ii) X is non-smooth and locally isotropic. For case (i), the expected Euler characteristic approximation is formulated explicitly; while for case (ii), it is shown that the asymptotics is similar to Pickands’ approximation on Euclidean space which involves Pickands’ constant and the volume of D. These extend the results in Cheng and Xiao (Bernoulli 22, 1113–1130 2016) from spheres to general Riemannian manifolds.

Original languageEnglish (US)
Pages (from-to)475-487
Number of pages13
JournalExtremes
Volume20
Issue number2
DOIs
StatePublished - Jun 1 2017
Externally publishedYes

Keywords

  • Euler characteristic
  • Excursion probability
  • Gaussian fields
  • Isotropic
  • Locally isotropic
  • Pickands’ constant
  • Riemannian manifolds

ASJC Scopus subject areas

  • Statistics and Probability
  • Engineering (miscellaneous)
  • Economics, Econometrics and Finance (miscellaneous)

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