Hawkes过程的总体观点
Population viewpoint on Hawkes processes
摘要：
研究了一类具有一般移民的线性Hawkes过程.这些是具有散粒噪声强度的计数过程，包括自激和外激模式。对于这样的过程，我们引入了年龄金字塔的概念，它根据移民和出生而演变。这种结合强度过程定义和分支表示的方法的优点是，人口年龄金字塔跟踪了所有过去的事件。这是用来计算新的分布性质的一类线性Hawkes过程一般移民推广流行的指数生育率函数。给出了Hawkes过程的路径构造及其基本种群.
英文摘要：
This paper focuses on a class of linear Hawkes processes with general immigrants. These are counting processes with shot noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept of age pyramid which evolves according to immigration and births. The virtue if this approach that combines an intensity process definition and a branching representation is that the population age pyramid keeps track of all past events. This is used to compute new distribution properties for a class of linear Hawkes processes with general immigrants which generalize the popular exponential fertility function. The pathwise construction of the Hawkes process and its underlying population is also given.
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