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 $\beta + 1 \in (1, 2 ]$, this replacement has the advantage that the Laplace transform of the Mittag-Leffler function is known explicitly, leading to simpler calculation of relevant quantities.
A Fractional Hawkes Process / Chen, J.; Hawkes, A. G.; Scalas, E.. - (2021), pp. 121-131. - SEMA SIMAI SPRINGER SERIES. [10.1007/978-3-030-69236-0_7].
A Fractional Hawkes Process
Scalas E.
2021
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 $\beta + 1 \in (1, 2 ]$, this replacement has the advantage that the Laplace transform of the Mittag-Leffler function is known explicitly, leading to simpler calculation of relevant quantities.File allegati a questo prodotto
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