A Fractional Hawkes process

A.G. Hawkes; E. Scalas; J. Chen

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A Fractional Hawkes process

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arxiv 2003.01027 v1 pith:T7KJ3RBO submitted 2020-03-02 math.PR math.STstat.TH

J. Chen , A.G. Hawkes , E. Scalas This is my paper · ORCID

classification math.PRmath.STstat.TH

keywords kernelmittag-leffleradvantagebetacalculationdecaysetasexplicitly

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

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