A Fractional Hawkes process

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

arxiv: 2003.01027 · v1 · pith:T7KJ3RBOnew · submitted 2020-03-02 · 🧮 math.PR · math.ST· stat.TH

A Fractional Hawkes process

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

classification 🧮 math.PR math.STstat.TH

keywords kernelmittag-leffleradvantagebetacalculationdecaysetasexplicitly

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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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A Fractional Hawkes process

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