Extremes of Gaussian Processes with Random Variance

Juerg Huesler (University of Bern)
Vladimir Piterbarg (Moscow Lomonosov State university)
Yueming Zhang (University of Bern)


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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Pages: 1254-1280

Publication Date: July 7, 2011

DOI: 10.1214/EJP.v16-904


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