论文标题
极限点过程和应用到极端簇的不变性属性
Invariance properties of limiting point processes and applications to clusters of extremes
论文作者
论文摘要
在极端价值理论的示例中，我们介绍了集群过程的一般概念，作为时间序列中某个事件回报的限制点过程。我们探讨了群集过程的一般不变特性，这些特性是在最小假设下的基础时间序列的平稳性所暗示的。群集大小分布特别令人感兴趣，我们在其中介绍了两个检查的和典型的群集大小的概念，并得出了它们之间的一般属性和连接。尽管极值理论中常用的极端指数通常被解释为“平均群集大小”的倒数，但我们指出，这仅适用于典型集群大小的期望值，这是由于续签理论中与检查悖论非常相似的效果所引起的。
Motivated by examples from extreme value theory we introduce the general notion of a cluster process as a limiting point process of returns of a certain event in a time series. We explore general invariance properties of cluster processes which are implied by stationarity of the underlying time series under minimal assumptions. Of particular interest are the cluster size distributions, where we introduce the two notions of inspected and typical cluster sizes and derive general properties of and connections between them. While the extremal index commonly used in extreme value theory is often interpreted as the inverse of a "mean cluster size", we point out that this only holds true for the expected value of the typical cluster size, caused by an effect very similar to the inspection paradox in renewal theory.
