Extremes of spherical fractional Brownian motion

Dan Cheng; Peng Liu

doi:10.1007/s10687-019-00344-4

Extremes of spherical fractional Brownian motion

Dan Cheng, Peng Liu

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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

Original language	English (US)
Pages (from-to)	433-457
Number of pages	25
Journal	Extremes
Volume	22
Issue number	3
DOIs	https://doi.org/10.1007/s10687-019-00344-4
State	Published - Sep 15 2019

Keywords

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)

Access to Document

10.1007/s10687-019-00344-4

Cite this

@article{af547fe31a0a47f1b32016cc175ec65e,

title = "Extremes of spherical fractional Brownian motion",

abstract = "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.",

keywords = "60G15, 60G70, Asymptotics, Excursion probability, Fractional Brownian motion, Gaussian random fields, Pickands constant, Piterbarg constant, SFBM, Sphere",

author = "Dan Cheng and Peng Liu",

note = "Funding Information: The authors thank Enkelejd Hashorva from University of Lausanne for his helpful discussions and suggestions, and thank anonymous referees for their careful reading and valuable comments. Publisher Copyright: {\textcopyright} 2019, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2019",

month = sep,

day = "15",

doi = "10.1007/s10687-019-00344-4",

language = "English (US)",

volume = "22",

pages = "433--457",

journal = "Extremes",

issn = "1386-1999",

publisher = "Springer Netherlands",

number = "3",

}

TY - JOUR

T1 - Extremes of spherical fractional Brownian motion

AU - Cheng, Dan

AU - Liu, Peng

N1 - Funding Information: The authors thank Enkelejd Hashorva from University of Lausanne for his helpful discussions and suggestions, and thank anonymous referees for their careful reading and valuable comments. Publisher Copyright: © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2019/9/15

Y1 - 2019/9/15

N2 - 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.

AB - 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.

KW - 60G15

KW - 60G70

KW - Asymptotics

KW - Excursion probability

KW - Fractional Brownian motion

KW - Gaussian random fields

KW - Pickands constant

KW - Piterbarg constant

KW - SFBM

KW - Sphere

UR - http://www.scopus.com/inward/record.url?scp=85062704159&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062704159&partnerID=8YFLogxK

U2 - 10.1007/s10687-019-00344-4

DO - 10.1007/s10687-019-00344-4

M3 - Article

AN - SCOPUS:85062704159

SN - 1386-1999

VL - 22

SP - 433

EP - 457

JO - Extremes

JF - Extremes

IS - 3

ER -

Extremes of spherical fractional Brownian motion

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this