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A Fractional Hawkes process

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 $β+ 1 \in (1,2]$, this replacement has the advantage that the Laplace transform of the Mittag-Leffler function is known explicitly, leading to simpler calculation of relevant quantities.

preprint2020arXivOpen access
J. ChenA. G. HawkesE. Scalas
math.PRmath.STStatistics Theory
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J. ChenA. G. HawkesE. Scalas

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