Remarks on Pickands theorem
Probability
2017-03-16 v3
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.
Cite
@article{arxiv.0904.3832,
title = {Remarks on Pickands theorem},
author = {Zbigniew Michna},
journal= {arXiv preprint arXiv:0904.3832},
year = {2017}
}