(1) 21 Via Carlo Alberta dalla Chiesa, 00061 Anguillara, Roma, Italy;(2) Institute of Statistics and Operations Research, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand
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.