scholarly journals Pickands’ constant $H_{\alpha}$ does not equal $1/\Gamma(1/\alpha)$, for small $\alpha$

Bernoulli ◽  
2017 ◽  
Vol 23 (1) ◽  
pp. 582-602 ◽  
Author(s):  
Adam J. Harper
Keyword(s):  
Pickands Constant

scholarly journals Pickands’ constant at first order in an expansion around Brownian motion

2017 ◽  
Vol 50 (16) ◽  
pp. 16LT04 ◽  
Author(s):  
Mathieu Delorme ◽  
Alberto Rosso ◽  
Kay Jörg Wiese
Keyword(s):  
Brownian Motion ◽  
First Order ◽  
Pickands Constant

scholarly journals Remarks on Pickands’ theorem

2018 ◽  
Vol 37 (2) ◽  
pp. 373-393 ◽  
Author(s):  
Zbigniew Michna
Keyword(s):  
Lower Bound ◽  
Gaussian Processes ◽  
Complete Proof ◽  
Pickands Constant ◽  
Stationary Gaussian Processes ◽  
Double Sum

REMARKS ON PICKANDS’ THEOREMIn this article we present the 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 the 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. Moreover, we review equivalent definitions, simulations and bounds of Pickands constant.

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