Remarks on Pickands’ theorem

• Autorzy: Michna Z.

Identyfikatory

DOI

10.19195/0208-4147.37.2.10

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

stationary Gaussian process; supremum of a process; Pickands constant; fractional Brownian motion

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2017
• Tom: Vol. 37, Fasc. 2
• Strony: 373--393
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Michna Z.

• Department of Mathematics and Cybernetics, Wrocław University of Economics, 53-345 Wrocław, Poland

Bibliografia

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Uwagi

To Professor Tomasz Rolski who has been dedicating his life to science.

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).