论文标题
关于随机簇的极端和标记的续订群集过程
On extremes of random clusters and marked renewal cluster processes
论文作者
论文摘要
文章描述了簇中的极端观测值的极限分布。我们首先研究单个群集的尾巴行为，然后应用开发的理论来确定$ \ max \ {x_j的限制分布：j = 0，\ ldots，k（t）\} $，其中$ k（t）$是i.i.d的数量。观察结果$（x_j）$根据一般标记的续订群集流程到达时间$ t $。结果在一些常用的泊松群集模型（例如标记的霍克斯过程）的背景下进行了说明。
The article describes the limiting distribution of the extremes of observations that arrive in clusters. We start by studying the tail behaviour of an individual cluster and then we apply the developed theory to determine the limiting distribution of $\max\{X_j: j=0,\ldots, K(t)\}$, where $K(t)$ is the number of i.i.d. observations $(X_j)$ arriving up to the time $t$ according to a general marked renewal cluster process. The results are illustrated in the context of some commonly used Poisson cluster models such as the marked Hawkes process.
