A fractional Hawkes process II: Further characterization of the process

Cassien Habyarimana, Jane A. Aduda, Enrico Scalas, Jing Chen, Alan G. Hawkes and Federico Polito

Physica A: Statistical Mechanics and its Applications, 2023, vol. 615, issue C

Abstract: We characterize a Hawkes point process with kernel proportional to the probability density function of Mittag-Leffler random variables. This kernel decays as a power law with exponent β+1∈(1,2]. Several analytical results can be proved, in particular for the expected intensity of the point process and for the expected number of events of the counting process. These analytical results are used to validate algorithms that numerically invert the Laplace transform of the expected intensity as well as Monte Carlo simulations of the process. Finally, Monte Carlo simulations are used to derive the full distribution of the number of events. The algorithms used for this paper are available at https://github.com/habyarimanacassien/Fractional-Hawkes.

Keywords: Point processes; Hawkes processes; Mittag-Leffler distribution; Fractional calculus (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:615:y:2023:i:c:s0378437123001516

DOI: 10.1016/j.physa.2023.128596

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