A fractional Hawkes process II: further characterization of the process

Chen, Jing ORCID: https://orcid.org/0000-0001-7135-2116, Scalas, Enrico, Habyarimana, Cassien, Polito, Federico, Hawkes, Alan G. and Aduda, Jane Akinyi 2023. A fractional Hawkes process II: further characterization of the process. Physica A 615 , 128596. 10.1016/j.physa.2023.128596

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Abstract

We characterize a Hawkes point process with kernel proportional to the prob- ability 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 trans- form 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Cardiff Institute of Society and Health (CISHE) Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Elsevier
ISSN:	1873-2119
Date of First Compliant Deposit:	2 March 2023
Date of Acceptance:	20 February 2023
Last Modified:	03 May 2023 07:46
URI:	https://orca.cardiff.ac.uk/id/eprint/157150

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