On extremal index of max-stable stationary processes

• Autorzy: Dębicki K. , Hashorva E.

Identyfikatory

DOI

10.19195/0208-4147.37.2.6

• Języki publikacji: EN

Abstrakty

EN

In this contribution we discuss the relation between Pickands-type constants defined for certain Brown-Resnick stationary proces W(t), t ϵ R, as [wzór] (set 0Z = R if δ = 0) and the extremal index of the associated max-stable stationary process ξ_W. We derive several new formulas and obtain lower bounds for Ή^δ_W if W is a Gaussian or a Lévy process. As a by-product we show an interesting relation between Pickands constants and lower tail probabilities for fractional Brownian motions.

Słowa kluczowe

EN

extremal index; mean cluster index; Pickands constant; M3 representation; Brown-Resnick stationary; max-stable process; Gaussian process; Lévy process

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2017
• Tom: Vol. 37, Fasc. 2
• Strony: 299--317
• Opis fizyczny: Bibliogr. 52 poz.

Twórcy

autor

Dębicki K.

• Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Hashorva E.

• University of Lausanne, Bâtiment Extranef, UNIL-Dorigny, 1015 Lausanne, Switzerland

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Uwagi

To Tomasz Rolski, thankful for all the support and ideas you shared with us!

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