A NEW PROOF OF AN OLD RESULT BY PICKANDS

作者：Albin J M P^*; Choi H

来源：Electronic Communications in Probability, 2010, 15: 339-345.

• Stationary Gaussian process
• Pickands constant
• extremes

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

• 出版日期2010-9-12