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Extremes of spherical fractional Brownian motion

Name: Extremes of spherical fractional Brownian motion
Keywords: Statistics and Probability; Engineering (miscellaneous); Economics, Econometrics and Finance (miscellaneous), Probability (math.PR), FOS: Mathematics, Mathematics - Probability

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 2019Embargo end date: 01 Jan 2018 United Kingdom Publisher:Springer Science and Business Media LLCJournal:Extremes, volume 22, pages 433-457 (issn: 1386-1999, eissn: 1572-915X,

Authors: Cheng, Dan; Liu, Peng;

doi: 10.1007/s10687-019-00344-4 , 10.48550/arxiv.1806.02965

arXiv: http://arxiv.org/abs/1806.02965

Extremes of spherical fractional Brownian motion

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Abstract

Let $\{B_��(x), x \in \mathbb{S}^N\}$ be a fractional Brownian motion on the $N$-dimensional unit sphere $\mathbb{S}^N$ with Hurst index $��$. We study the excursion probability $\mathbb{P}\{\sup_{x\in T} B_��(x) > u \}$ and obtain the asymptotics as $u\to \infty$, where $T$ can be the entire sphere $\mathbb{S}^N$ or a geodesic disc on $\mathbb{S}^N$.

Country

United Kingdom

Related Organizations

University of Essex
United Kingdom
The University of Texas System
United States
Arizona State University
United States
University of Lausanne
Switzerland

Keywords

Statistics and Probability; Engineering (miscellaneous); Economics, Econometrics and Finance (miscellaneous), Probability (math.PR), FOS: Mathematics, Mathematics - Probability

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NSF| Collaborative Research: Critical Points and Excursion Probability of Random Fields: Theory and Statistical Applications