Habyarimana, Cassien, Aduda, Jane A, Scalas, Enrico, Chen, Jing, Hawkes, Alan G and Polito, Federico (2023) A fractional Hawkes process II: further characterization of the process. Physica A: Statistical Mechanics and its Applications, 615. pp. 1-11. ISSN 0378-4371

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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 $\beta +1 \in (1,2]$. 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 {\tt https://github.com/habyarimanacassien/Fractional-Hawkes}.

Item Type:	Article
Schools and Departments:	School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor:	Mx Elements Account
Depositing User:	Mx Elements Account
Date Deposited:	21 Feb 2023 10:17
Last Modified:	27 Apr 2023 12:58
URI:	http://sro.sussex.ac.uk/id/eprint/110811

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