Open AccessPhysicsMathematics

A Fractional Hawkes process

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

2020.3.2SEMA SIMAI Springer Series

DOI: 10.1007/978-3-030-69236-0_7

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 β + 1 ∈ (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

Citation format

CHEN, J.; HAWKES, A. G.; SCALAS, E. A fractional hawkes process [preprint]. arXiv, 2020. arXiv:2003.01027.