论文标题
霍克斯累积物的递归计算
Recursive computation of the Hawkes cumulants
论文作者
论文摘要
我们提出了一种基于标准组合工具（例如贝尔多项式）的霍克斯类型自我激发点过程累积物的累积方法的递归方法。与基于微分方程，树木枚举或Martingale参数相比，这种封闭形式的方法更容易在高阶累积物上实施。结果通过蒙特卡洛模拟证实，也适用于通过多维自我激发过程产生的关节累积物的计算。
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.
