A New Proof of an Old Result by Pickands
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

Author

Patrik Albin

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

H. Choi

Electronic Communications in Probability

1083589x (eISSN)

Vol. 15 339-345

Subject Categories

Probability Theory and Statistics

DOI

10.1214/ECP.v15-1566

More information

Created

10/8/2017