Electronic Journal of Probability

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

Juerg Huesler, Anna Ladneva, and Vladimir Piterbarg

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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.

Article information

Electron. J. Probab., Volume 15 (2010), paper no. 59, 1825-1862.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60G15: Gaussian processes 60G10: Stationary processes

Gaussian process extreme values clusters separated clusters asymptotic behavior correlation function

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Huesler, Juerg; Ladneva, Anna; Piterbarg, Vladimir. On Clusters of High Extremes of Gaussian Stationary Processes with $\varepsilon$-Separation. Electron. J. Probab. 15 (2010), paper no. 59, 1825--1862. doi:10.1214/EJP.v15-828. https://projecteuclid.org/euclid.ejp/1464819844

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