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Limit laws on extremes of nonhomogeneous Gaussian random fields

Part of: Stochastic processes

Published online by Cambridge University Press:  15 September 2017

Zhongquan Tan
Zhongquan Tan*
Affiliation:
Zhejiang University and Jiaxing University
*
* Postal address: College of Mathematics, Physics and Information Engineering, Jiaxing University, Lianglin Campus, Jiaxing, 314001, P.R. China. Email address: [email protected]
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Abstract

In this paper, by using the tail asymptotics derived by Dębicki et al. (2016), we prove the Gumbel limit laws for the maximum of a class of nonhomogeneous Gaussian random fields. As an application of the main results, we derive the Gumbel limit law for Shepp statistics of fractional Brownian motion and Gaussian integrated processes.

Keywords

ExtremesGumbel limit lawnonhomogeneous Gaussian random fieldShepp statisticfractional Brownian motion

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 60G70: Extreme value theory; extremal processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 811 - 832
Copyright
Copyright © Applied Probability Trust 2017 

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