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A Fractional Hawkes process

Published 2 Mar 2020 in math.PR, math.ST, and stat.TH | (2003.01027v1)

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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Authors (3)

  1. J. Chen 
  2. A. G. Hawkes 
  3. E. Scalas 

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