Journal article, 2010

Let {xi(t)}(t is an element of[0,h]) be a stationary Gaussian process with covariance function r such that r(t) = 1 - C vertical bar t vertical bar(alpha) + o(vertical bar t vertical bar(alpha)) as t -> 0. We give a new and direct proof of a result originally obtained by Pickands, on the asymptotic behaviour as u -> infinity of the probability P{sup(t is an element of vertical bar 0,h vertical bar) 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

asymptotic properties

stationary-processes

Stationary Gaussian process

gaussian process

tails

Pickands constant

extremes

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

1083-589X (ISSN)

Vol. 15 339-345Probability Theory and Statistics

10.1214/ECP.v15-1566