We consider a spatial Lévy-driven moving average with an underlying Lévy measure having a subexponential right tail, which is also in the maximum domain of attraction of the Gumbel distribution. Assuming that the left tail is not heavier than the right tail, and that the integration kernel satisfies certain regularity conditions, we show that the supremum of the field over any bounded set has a right tail equivalent to that of the Lévy measure. Furthermore, for a very general class of expanding index sets, we show that the running supremum of the field, under a suitable scaling, converges to the Gumbel distribution.

中文翻译：

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Gumbel 吸引力域中次指数 Lévy 驱动的随机场的极值

我们考虑一个空间 Lévy 驱动的移动平均线，其基础 Lévy 测度具有次指数右尾，这也在 Gumbel 分布的最大吸引力域中。假设左尾不比右尾重，并且积分核满足一定的正则条件，我们证明在任何有界集合上的域的上界都有一个与 Lévy 测度相等的右尾。此外，对于一类非常普遍的扩展索引集，我们表明该领域的运行最高，在适当的缩放比例下，收敛到 Gumbel 分布。