霍克斯模型及其应用
Hawkes Models And Their Applications
AI总结：
本文对具有自激发特性的霍克斯过程及其多类推广形式进行系统性综述，涵盖模型构建、仿真算法与关键文献指引，梳理其在地震学、金融学等多领域的应用。
摘要：
霍克斯过程是一种用于统计系统中到达事件数量的模型，具有自激发特性——即一次到达会提升近期内发生更多到达事件的概率。该模型及其推广形式已被应用于众多不同领域，其中发展尤为成熟的两类应用分别在地震学和金融学领域。由于原始模型简洁优美，研究者们提出了多种推广形式，包括：为每次到达标记标记量、多变量形式、含空间分量形式、由更新过程驱动的形式、离散时间形式等等。本文对传统霍克斯模型及现代推广形式进行了系统性综述，详细介绍其构建方式、仿真算法，并给出了可供深入研究的相关关键文献指引。
英文摘要：
The Hawkes process is a model for counting the number of arrivals to a system which 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 which: track marks for each arrival, are multivariate, have a spatial component, are driven by renewal processes, treat time as discrete, and so on. This paper creates a cohesive review of the traditional Hawkes model and the modern generalizations, providing details on their construction, simulation algorithms, and giving key references to the appropriate literature for a detailed treatment.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
