The Hawkes process is a model for counting the number of arrivals to a system that exhibits the self-exciting property—that one arrival creates a heightened chance of further arrivals in the near future. The model and its generalizations have been applied in a plethora of disparate domains, though two particularly developed applications are in seismology and in finance. As the original model is elegantly simple, generalizations have been proposed that track marks for each arrival, are multivariate, have a spatial component, are driven by renewal processes, treat time as discrete, and so on. This article creates a cohesive review of the traditional Hawkes model and the modern generalizations, providing details on their construction and simulation algorithms, and giving key references to the appropriate literature for a detailed treatment.

中文翻译：

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Hawkes 模型及其应用


Hawkes 过程是一个模型，用于计算系统到达的数量，该系统表现出自我激励的属性，即一次到达在不久的将来创造更多到达的机会。该模型及其泛化已应用于大量不同的领域，尽管两个特别开发的应用是地震学和金融学。由于原始模型非常简单，因此提出了以下概括：每次到达的轨迹标记是多变量的，具有空间成分，由更新过程驱动，将时间视为离散的，等等。本文对传统 Hawkes 模型和现代泛化进行了有凝聚力的回顾，提供了它们的构造和模拟算法的详细信息，并为适当的文献提供了关键参考以进行详细处理。