Abstract
This paper describes a generalization of Hawkes' self-exciting process in which each event creates a process of “offspring” with conditional intensity governed by a diffusion kernel. The process may be described as a space-time branching process with immigration, the immigration representing a background series of independent events. The model can be fitted by likelihood methods. As an illustration it is fitted to the catalogue of historical Italian earthquakes.
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Musmeci, F., Vere-Jones, D. A space-time clustering model for historical earthquakes. Ann Inst Stat Math 44, 1–11 (1992). https://doi.org/10.1007/BF00048666
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DOI: https://doi.org/10.1007/BF00048666