(Received December 21, 1989; revised November 5, 1990)
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.
Key words and phrases: Space-time models, cluster point processes, earthquake modelling, self-exciting process, spatial branching process, epidemic models.
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