Numerical method for means of linear Hawkes processes |
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Authors: | Zhongping Li Lirong Cui |
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Affiliation: | 1. School of Management and Economics, Beijing Institute of Technology, Beijing, Chinazhongpingli666@163.com;3. School of Management and Economics, Beijing Institute of Technology, Beijing, China |
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Abstract: | AbstractLinear 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. |
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Keywords: | Linear Hawkes process Laplace transform Inverse Laplace transform Mean WeChat network |
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