A fractional Hawkes process

Chen, J, Hawkes, A G and Scalas, E (2021) A fractional Hawkes process. In: Beghin, Luisa, Mainardi, Francesco and Garrappa, Roberto (eds.) Nonlocal and fractional operators. SEMA SIMAI Springer Series, 26 . Springer International Publishing, pp. 121-131. ISBN 9783030692353

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Abstract

We modify ETAS models by replacing the Pareto-like kernel proposed by Ogata with a Mittag-Leffler type kernel. Provided that the kernel decays as a power law with exponent β+1∈(1,2] , this replacement has the advantage that the Laplace transform of the Mittag-Leffler function is known explicitly, leading to simpler calculation of relevant quantities.

Item Type: Book Section
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 04 May 2021 06:53
Last Modified: 29 Jul 2021 15:35
URI: http://sro.sussex.ac.uk/id/eprint/90839

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