For a given stationary max-stable random field X(t), t ∈ ℤ^d, the corresponding generalized Pickands constant coincideswith the classical extremal index θ_X ∈ [0, 1]. In this contribution,we discuss necessary and sufficient conditions for θ_X to be 0, positive, or equal to 1 and also show that θ_X 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 θ_X.

中文翻译：

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最大稳定随机场的极值指标

对于给定的固定的最大稳定随机场X（吨），吨∈ℤ ^d，相应的广义Pickands恒定coincideswith经典极值指标θ _X ∈[0 ， 1]。在此贡献中，我们讨论的充分必要条件为θ _X为0，正，或等于1，并且还表明，θ _X是等于所谓的块极值指标。此外，我们考虑的一些基本功能指标X和证明一大类函，他们用一致的θ _X。