Remarks on Pickands' theorem

Zbigniew Michna

Abstract

In 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
Author Zbigniew Michna (MISaF / IZM / KMiC)
Zbigniew Michna,,
- Katedra Matematyki i Cybernetyki
Journal seriesProbability and Mathematical Statistics, ISSN 0208-4147, e-ISSN 2300-8113, (A 15 pkt)
Issue year2017
Vol37
No2
Pages373-393
Publication size in sheets1
Keywords in EnglishStationary Gaussian process, supremum of a process, Pickands constant, fractional Brownian motion
ASJC Classification2613 Statistics and Probability
DOIDOI:10.19195/0208-4147.37.2.10
URL http://www.math.uni.wroc.pl/~pms/files/37.2/Article/37.2.10.pdf
Languageen angielski
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Michna_Remarks_ on_ Pickands'_ theorem2017.pdf 125,01 KB
Score (nominal)15
Score sourcejournalList
Publication indicators Scopus Citations = 6; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 0.448; WoS Impact Factor: 2017 = 0.286 (2) - 2017=0.345 (5)
Citation count*28 (2019-11-29)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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