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A new proof of an old result by Pickands

   
@article{ECP1566,
	author = {J.M.P. Albin and Hyemi Choi},
	title = {A new proof of an old result by Pickands},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {15},
	year = {2010},
	keywords = {Stationary Gaussian process; Pickands constant; extremes},
	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 $H_\alpha$.},
	pages = {no. 32, 339-345},
	issn = {1083-589X},
	doi = {10.1214/ECP.v15-1566},    
        url = {http://ecp.ejpecp.org/article/view/1566}}