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Moments for Hawkes Processes with Gamma Decay Kernel Functions

Author

Listed:
  • Lirong Cui

    (Qingdao University)

  • Bei Wu

    (Northwestern Polytechnical University)

  • Juan Yin

    (School of Management & Economics, Beijing Institute of Technology)

Abstract

Hawkes processes have been widely studied, but their many probability properties are still difficult to obtain, including their moments. In the paper, we shall give the moments for two classes of linear Hawkes processes with Gamma decay kernel and compound Gamma decay kernel functions by employing the method proposed by Cui et al. (2020), and the relationship between our results and those obtained by employing Dynkin’s formula is studied. Finally, the computation complexity of numbers of first-order linear differential equations is considered.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-020-09840-8
    DOI: 10.1007/s11009-020-09840-8
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    References listed on IDEAS

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