Moments for Hawkes Processes with Gamma Decay Kernel Functions

Lirong Cui (), Bei Wu and Juan Yin
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Lirong Cui: Qingdao University
Bei Wu: Northwestern Polytechnical University
Juan Yin: School of Management & Economics, Beijing Institute of Technology

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 3, 1565-1601

Abstract: 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.

Keywords: Hawkes process; Moments; Gamma decay kernel function; Compound gamma decay kernel function; Dynkin’s formula (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-020-09840-8

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