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A New Proof of an Old Result by Pickands

Patrik Albin (Institutionen för matematiska vetenskaper, matematisk statistik) ; H. Choi
Electronic Communications in Probability (1083-589X). Vol. 15 (2010), p. 339-345.
[Artikel, refereegranskad vetenskaplig]

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

Nyckelord: Stationary Gaussian process, Pickands constant, extremes, asymptotic properties, stationary-processes, gaussian process, tails



Denna post skapades 2011-03-31. Senast ändrad 2015-07-02.
CPL Pubid: 138459

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Matematisk statistik

Chalmers infrastruktur