论文标题
Lévy驱动的空间随机场的极端具有定期变化的Lévy度量
Extremes of Lévy-driven spatial random fields with regularly varying Lévy measure
论文作者
论文摘要
我们考虑一个由$ \ mathbb {r}^d $，$ d \ in \ mathbb {n} $索引的无限分开的随机字段，作为lévy基础的内核功能的积分，其具有lévy的基础，其lévy措施具有正常变化的右尾部。首先，我们证明其上限的尾部在任何有限的集合上都渐近地等同于Lévy测量时间的右尾部，即核的积分。其次，当通过适当增加连续索引集的序列观察该田地时，我们获得了一个极端值定理，表明运行的超符号会在分布中收敛到fréchet分布。
We consider an infinitely divisible random field indexed by $\mathbb{R}^d$, $d\in\mathbb{N}$, given as an integral of a kernel function with respect to a Lévy basis with a Lévy measure having a regularly varying right tail. First we show that the tail of its supremum over any bounded set is asymptotically equivalent to the right tail of the Lévy measure times the integral of the kernel. Secondly, when observing the field over an appropriately increasing sequence of continuous index sets, we obtain an extreme value theorem stating that the running supremum converges in distribution to the Fréchet distribution.
