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On Extremal Index of Max-Stable Random Fields

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Abstract

For a given stationary max-stable random field X(t), t ∈ ℤd, the corresponding generalized Pickands constant coincideswith the classical extremal index θX ∈ [0, 1]. In this contribution,we discuss necessary and sufficient conditions for θX to be 0, positive, or equal to 1 and also show that θX is equal to the so-called block extremal index. Further, we consider some general functional indices of X and prove that for a large class of functionals they coincide with θX.

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  1. University of Lausanne, Chamberonne, 1015, Lausanne, Switzerland

    Enkelejd Hashorva

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Partially supported by SNSF grants 200021-175752/1 and 200021-196888.

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Hashorva, E. On Extremal Index of Max-Stable Random Fields. Lith Math J 61, 217–238 (2021). https://doi.org/10.1007/s10986-021-09519-8

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