Remarks on Pickands theorem
Abstract
In this article we present Pickands theorem and his double sum method. We follow Piterbarg's proof of this theorem. Since his proof relies on general lemmas we present a complete proof of Pickands theorem using Borell inequality and Slepian lemma. The original Pickands proof is rather complicated and is mixed with upcrossing probabilities for stationary Gaussian processes. We give a lower bound for Pickands constant.
 Publication:

arXiv eprints
 Pub Date:
 April 2009
 arXiv:
 arXiv:0904.3832
 Bibcode:
 2009arXiv0904.3832M
 Keywords:

 Mathematics  Probability;
 60G15 (Primary);
 60G70 (Secondary)