2024/02/29 by Louis Davis, Boris Baeumer, Davis, Louis +3
Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #Fractional Differential Equations Solutions #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2403.00142
openalex publication_date 2024/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.