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Numerical method for means of linear Hawkes processes

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  • Zhongping Li
  • Lirong Cui

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.

Suggested Citation

  • Zhongping Li & Lirong Cui, 2020. "Numerical method for means of linear Hawkes processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(15), pages 3681-3697, August.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:15:p:3681-3697
    DOI: 10.1080/03610926.2020.1713374
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    Cited by:

    1. Dharmaraja Selvamuthu & Paola Tardelli, 2022. "Infinite-server systems with Hawkes arrivals and Hawkes services," Queueing Systems: Theory and Applications, Springer, vol. 101(3), pages 329-351, August.
    2. Lirong Cui & Bei Wu & Juan Yin, 2022. "Moments for Hawkes Processes with Gamma Decay Kernel Functions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1565-1601, September.

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