Open Access
2010 On Clusters of High Extremes of Gaussian Stationary Processes with $\varepsilon$-Separation
Juerg Huesler, Anna Ladneva, Vladimir Piterbarg
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Electron. J. Probab. 15: 1825-1862 (2010). DOI: 10.1214/EJP.v15-828


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.


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Juerg Huesler. Anna Ladneva. Vladimir Piterbarg. "On Clusters of High Extremes of Gaussian Stationary Processes with $\varepsilon$-Separation." Electron. J. Probab. 15 1825 - 1862, 2010.


Accepted: 14 November 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1226.60082
MathSciNet: MR2738340
Digital Object Identifier: 10.1214/EJP.v15-828

Primary: 60G70
Secondary: 60G10 , 60G15

Keywords: asymptotic behavior , Clusters , correlation function , Extreme values , Gaussian process , separated clusters

Vol.15 • 2010
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