We propose a recursive method for the computation of the cumulants of self-exciting point processes of Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement on higher-order cumulants in comparison with existing methods based on differential equations, tree enumeration or martingale arguments. The results are corroborated by Monte Carlo simulations, and also apply to the computation of joint cumulants generated by multidimensional self-exciting processes.

中文翻译：

---

霍克斯累积量的递归计算

我们提出了一种基于标准组合工具（例如贝尔多项式）的递归方法，用于计算霍克斯类型的自激点过程的累积量。与基于微分方程、树枚举或鞅参数的现有方法相比，这种封闭形式的方法更容易在高阶累积量上实现。结果得到了蒙特卡罗模拟的证实，也适用于多维自激过程产生的联合累积量的计算。