Extremes of spherical fractional Brownian motion

Dan Cheng, Peng Liu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Let { Bβ(x) , x∈ SN} be a fractional Brownian motion on the N-dimensional unit sphere SN with Hurst index β. We study the excursion probability ℙ{ supx TBβ(x) > u} and obtain the asymptotics as u →∞, where T can be the entire sphere SN or a geodesic disc on SN.

Original languageEnglish (US)
Pages (from-to)433-457
Number of pages25
Issue number3
StatePublished - Sep 15 2019


  • 60G15
  • 60G70
  • Asymptotics
  • Excursion probability
  • Fractional Brownian motion
  • Gaussian random fields
  • Pickands constant
  • Piterbarg constant
  • SFBM
  • Sphere

ASJC Scopus subject areas

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


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