English

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.

Keywords

Cite

@article{arxiv.0904.3832,
  title  = {Remarks on Pickands theorem},
  author = {Zbigniew Michna},
  journal= {arXiv preprint arXiv:0904.3832},
  year   = {2017}
}
R2 v1 2026-06-21T12:54:45.336Z