论文标题
极端聚类在适度的远距离依赖性和中等沉重的尾巴下
Extremal clustering under moderate long range dependence and moderately heavy tails
论文作者
论文摘要
我们研究了固定序列中极端的聚类，并在gumbel的最大吸引力域中具有亚指数尾巴，我们在随机sup测量和空间$ d（0，\ infty）$中获得功能极限定理。如果内存仅适度长，则极限具有牙龈分布。但是，正如我们的结果相当引人注目的那样，即使在适度的长距离依赖设置中，“一次大跳跃的启发式”也可能失败。随着尾巴变得更轻，固定过程的极端行为可能取决于驱动噪声的多个大值。
We study clustering of the extremes in a stationary sequence with subexponential tails in the maximum domain of attraction of the Gumbel We obtain functional limit theorems in the space of random sup-measures and in the space $D(0,\infty)$. The limits have the Gumbel distribution if the memory is only moderately long. However, as our results demonstrate rather strikingly, the "heuristic of a single big jump" could fail even in a moderately long range dependence setting. As the tails become lighter, the extremal behavior of a stationary process may depend on multiple large values of the driving noise.
