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2010 A new proof of an old result by Pickands
J.M.P. Albin, Hyemi Choi
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Electron. Commun. Probab. 15: 339-345 (2010). DOI: 10.1214/ECP.v15-1566

Abstract

Let $\{\xi(t)\}_{t\in[0,h]}$ be a stationary Gaussian process with covariance function $r$ such that $r(t) =1-C|t|^{\alpha}+o(|t|^{\alpha})$ as $t\to0$. We give a new and direct proof of a result originally obtained by Pickands, on the asymptotic behaviour as $u\to\infty$ of the probability $\Pr\{\sup_{t\in[0,h]}\xi(t)>u\}$ that the process $\xi$ exceeds the level $u$. As a by-product, we obtain a new expression for Pickands constant $H_\alpha$.

Citation

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J.M.P. Albin. Hyemi Choi. "A new proof of an old result by Pickands." Electron. Commun. Probab. 15 339 - 345, 2010. https://doi.org/10.1214/ECP.v15-1566

Information

Accepted: 12 September 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1227.60068
MathSciNet: MR2685014
Digital Object Identifier: 10.1214/ECP.v15-1566

Subjects:
Primary: 60G70
Secondary: 60G15

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