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2011 Extremes of Gaussian Processes with Random Variance
Juerg Huesler, Vladimir Piterbarg, Yueming Zhang
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Electron. J. Probab. 16: 1254-1280 (2011). DOI: 10.1214/EJP.v16-904

Abstract

Let $\xi(t)$ be a standard locally stationary Gaussian process with covariance function $1-r(t,t+s)\sim C(t)|s|^\alpha$ as $s\to0$, with $0<\alpha\leq 2$ and $C(t)$ a positive bounded continuous function. We are interested in the exceedance probabilities of $\xi(t)$ with a random standard deviation $\eta(t)=\eta-\zeta t^\beta$, where $\eta$ and $\zeta$ are non-negative bounded random variables. We investigate the asymptotic behavior of the extreme values of the process $\xi(t)\eta(t)$ under some specific conditions which depends on the relation between $\alpha$ and $\beta$.

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Juerg Huesler. Vladimir Piterbarg. Yueming Zhang. "Extremes of Gaussian Processes with Random Variance." Electron. J. Probab. 16 1254 - 1280, 2011. https://doi.org/10.1214/EJP.v16-904

Information

Accepted: 7 July 2011; Published: 2011
First available in Project Euclid: 1 June 2016

MathSciNet: MR2827458
Digital Object Identifier: 10.1214/EJP.v16-904

Subjects:
Primary: 60G15
Secondary: 60F05 , 60G70

Keywords: Extremes , fractional Brownian motions , Gaussian processes , Locally stationary , random variance , ruin probability

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