A novel multidimensional fractional Hawkes process with magnitude discretization and Mittag-Leffler kernels outperforms the ETAS model on information criteria, residual diagnostics, and retrospective prediction for Japan and Middle America Trench earthquake datasets containing multiple mainshock–aft
A Fractional Model for Earthquakes
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abstract
This paper extends the existing fractional Hawkes process to better model mainshock-aftershock sequences of earthquakes. The fractional Hawkes process is a self-exciting point process model with temporal decay kernel being a Mittag-Leffler function. A maximum likelihood estimation scheme is developed and its consistency is checked. It is then compared to the ETAS model on three earthquake sequences in Southern California. The fractional Hawkes process performs favourably against the ETAS model. Additionally, two parameters in the fractional Hawkes process may have a fixed geophysical meaning dependent on the study zone and the stage of the seismic cycle the zone is in.
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A Multidimensional Fractional Hawkes Process for Multiple Earthquake Mainshock Aftershock Sequences
A novel multidimensional fractional Hawkes process with magnitude discretization and Mittag-Leffler kernels outperforms the ETAS model on information criteria, residual diagnostics, and retrospective prediction for Japan and Middle America Trench earthquake datasets containing multiple mainshock–aft