# Remarks on Pickands theorem

@inproceedings{Michna2009RemarksOP, title={Remarks on Pickands theorem}, author={Zbigniew Michna}, year={2009} }

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.

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## Pickands-Piterbarg constants for self-similar Gaussian processes

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## Pickands' constant at first order in an expansion around Brownian motion

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