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


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 $H_\alpha$.


Download Citation

J.M.P. Albin. Hyemi Choi. "A new proof of an old result by Pickands." Electron. Commun. Probab. 15 339 - 345, 2010.


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

Primary: 60G70
Secondary: 60G15

Keywords: Extremes , Pickands constant , stationary Gaussian process

Back to Top