Numerical method for means of linear Hawkes processes

Abstract

Linear Hawkes processes are widely used in many fields and means are the basic and critical information of them. However, there is little research on linear Hawkes processes’ means. In this paper, we present a numerical method based on the Laplace transform and inverse Laplace transform for means of linear Hawkes processes. The advantage of this method is that whatever the kernel function is, we can always obtain the numerical solutions of means for a linear Hawkes process. In addition, this numerical method provides the basic information of linear Hawkes processes by means. As an application, the numerical method is applied in a WeChat network model.

Keywords:

• Linear Hawkes process; Laplace transform; Inverse Laplace transform; Mean; WeChat network

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under grants 71871021 and 71631001.