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Extremes of Gaussian Processes with Random Variance


 
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1. Title Title of document Extremes of Gaussian Processes with Random Variance
 
2. Creator Author's name, affiliation, country Juerg Huesler; University of Bern; Switzerland
 
2. Creator Author's name, affiliation, country Vladimir Piterbarg; Moscow Lomonosov State university; Russian Federation
 
2. Creator Author's name, affiliation, country Yueming Zhang; University of Bern; Switzerland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Gaussian processes; locally stationary; ruin probability; random variance; extremes; fractional Brownian motions
 
3. Subject Subject classification 60G15; 60G70; 60F05
 
4. Description 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 $\beta$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2011-07-07
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/904
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-904
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
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