论文标题
竞争风险对霍克斯流程的解释
A competing risks interpretation of Hawkes processes
论文作者
论文摘要
我们将霍克斯流程的构造作为分段竞争风险模型。我们认为，自我激发核的最自然解释是有缺陷的随机变量的危害函数。这建立了该过程的所需定性特征与内核的参数形式之间的联系，我们使用文献中的示例为此进行了说明。提出了两个从生存分析文献中获得的治愈率模型的家族，作为自我激发核的新模型。最后，我们表明，竞争风险的观点会导致一般的仿真算法，该算法避免反转点过程的补偿器或执行接受拒绝步骤，因此是快速且相当一般的。
We give a construction of the Hawkes process as a piecewise competing risks model. We argue that the most natural interpretation of the self-excitation kernel is the hazard function of a defective random variable. This establishes a link between desired qualitative features of the process and a parametric form for the kernel, which we illustrate using examples from the literature. Two families of cure rate models taken from the survival analysis literature are proposed as new models for the self-excitation kernel. Finally, we show that the competing risks viewpoint leads to a general simulation algorithm which avoids inverting the compensator of the point process or performing an accept-reject step, and is therefore fast and quite general.
