A New Proof of an Old Result by Pickands
Artikel i vetenskaplig tidskrift, 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 Gaussian process

gaussian process


Pickands constant



Patrik Albin

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

H. Choi

Electronic Communications in Probability

1083-589X (ISSN)

Vol. 15 339-345


Sannolikhetsteori och statistik