论文标题
分数霍克斯过程II：进一步表征该过程
A fractional Hawkes process II: Further characterization of the process
论文作者
论文摘要
我们表征了鹰派点过程，其内核与Mittag-Leffler随机变量的概率密度函数成正比。 This kernel decays as a power law with exponent $β+1 \in (1,2]$. Several analytical results can be proved, in particular for the expected intensity of the point process and for the expected number of events of the counting process. These analytical results are used to validate algorithms that numerically invert the Laplace transform of the expected intensity as well as Monte Carlo simulations of the process. Finally, Monte Carlo simulations are used to derive可在{\ tt https://github.com/habyarimanacassien/fractional-hawkes}上获得的事件数量的完整分布。
We characterize a Hawkes point process with kernel proportional to the probability density function of Mittag-Leffler random variables. This kernel decays as a power law with exponent $β+1 \in (1,2]$. Several analytical results can be proved, in particular for the expected intensity of the point process and for the expected number of events of the counting process. These analytical results are used to validate algorithms that numerically invert the Laplace transform of the expected intensity as well as Monte Carlo simulations of the process. Finally, Monte Carlo simulations are used to derive the full distribution of the number of events. The algorithms used for this paper are available at {\tt https://github.com/habyarimanacassien/Fractional-Hawkes}.
