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On Clusters of High Extremes of Gaussian Stationary Processes with $\varepsilon$-Separation


 
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1. Title Title of document On Clusters of High Extremes of Gaussian Stationary Processes with $\varepsilon$-Separation
 
2. Creator Author's name, affiliation, country Juerg Huesler; University of Bern; Switzerland
 
2. Creator Author's name, affiliation, country Anna Ladneva; Moscow Lomonosov State University; Russian Federation
 
2. Creator Author's name, affiliation, country Vladimir Piterbarg; Moscow Lomonosov State University; Russian Federation
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Gaussian process; extreme values; clusters; separated clusters; asymptotic behavior; correlation function
 
3. Subject Subject classification 60G70; 60G15; 60G10
 
4. Description Abstract The clustering of extremes values of a stationary Gaussian process $X(t),t\in[0,T]$ is considered, where at least two time points of extreme values above a high threshold are separated by at least a small positive value $\varepsilon$. Under certain assumptions on the correlation function of the process, the asymptotic behavior of the probability of such a pattern of clusters of exceedances is derived exactly where the level to be exceeded by the extreme values, tends to $\infty$. The excursion behaviour of the paths in such an event is almost deterministic and does not depend on the high level $u$. We discuss the pattern and the asymptotic probabilities of such clusters of exceedances.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Swiss National Science Foundation; RFFI Grant 07-01-00077 of Russian Federation, grant DFG 436 RUS 113/722
 
7. Date (YYYY-MM-DD) 2010-11-14
 
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/828
 
10. Identifier Digital Object Identifier 10.1214/EJP.v15-828
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 15
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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