A SPACE-TIME CLUSTERING MODEL FOR HISTORICAL EARTHQUAKES

F. MUSMECI^{1} AND D. VERE-JONES^{2}

121 Via Carlo Alberta dalla Chiesa, 00061 Anguillara, Roma, Italy 2Institute of Statistics and Operations Research, Victoria University of Wellington,

P.O. Box 600, Wellington, New Zealand

(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.