论文标题
广义的多元鹰队流程
Generalized Multivariate Hawkes Processes
论文作者
论文摘要
这项工作有助于霍克斯流程的理论和应用。我们介绍并检查了一个新的鹰派过程，我们称之为广义霍克斯流程及其特殊的子类 - 广义的多元霍克斯流程（GMHP）。 GMHP是多元标记的点过程，它为（经典）多元霍克斯流程的家族添加了重要特征：它们允许明确地建模来自不同来源的激发事件，即由多元过程的不同坐标引起的激发事件。我们研究了广义霍克斯流程的存在问题，并提供了特定的广义多元霍克斯过程的构造。我们研究了GMHP的马尔可夫方面，并指出了GMHP的一些合理的重要应用。
This work contributes to the theory and applications of Hawkes processes. We introduce and examine a new class of Hawkes processes that we call generalized Hawkes processes, and their special subclass -- the generalized multivariate Hawkes processes (GMHPs). GMHPs are multivariate marked point processes that add an important feature to the family of the (classical) multivariate Hawkes processes: they allow for explicit modelling of simultaneous occurrence of excitation events coming from different sources, i.e. caused by different coordinates of the multivariate process. We study the issue of existence of a generalized Hawkes process, and we provide a construction of a specific generalized multivariate Hawkes process. We investigate Markovian aspects of GMHPs, and we indicate some plausible important applications of GMHPs.
