论文标题
关于最大稳定随机字段的极端指数
On Extremal Index of Max-Stable Random Fields
论文作者
论文摘要
对于给定的固定最大稳定随机字段$ x（t），t \ in z^d $，相应的广义pickands常数与始终存在的经典极端索引$θ$相吻合。在此贡献中，我们讨论了$θ$为0，正或等于1的必要条件，还表明$θ$等于所谓的块极端指数。此外，我们考虑了一些$ x $的一般功能索引，并证明对于大量的功能，它们与$θ$相吻合。我们对最大稳定和固定随机场的研究很重要，因为公式有效，对多元定期变化随机场的候选极端指数进行了明显的修改。
For a given stationary max-stable random field $X(t),t\in Z^d$ the corresponding generalised Pickands constant coincides with the classical extremal index $θ$ which always exists. In this contribution we discuss necessary and sufficient conditions for $θ$ to be 0, positive or equal to 1 and also show that $θ$ 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 $θ$. Our study of max-stable and stationary random fields is important since the formulas are valid with obvious modifications for the candidate extremal index of multivariate regularly varying random fields.
