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On extremal index of max-stable stationary processes

Dębicki K., Hashorva E.

Probability and Mathematical Statistics

2017

Vol. 37, Fasc. 2

299--317

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 ξW. We derive several new formulas and obtain lower bounds for ΉδW 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.