A New Proof of an Old Result by Pickands

• 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

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

Stationary Gaussian process

Pickands constant

extremes

asymptotic properties

stationary-processes

gaussian process

tails

asymptotic properties

Publication and Content Type

ref (subject category)

art (subject category)