In this article we obtain rates of convergence to equilibrium of marked Hawkes processes in two situations. Firstly, the stationary process is the empty process, in which case we speak of the rate of extinction. Secondly, the stationary process is the unique stationary and nontrivial marked Hawkes process, in which case we speak of the rate of installation. The first situation models small epidemics, whereas the results in the second case are useful in deriving stopping rules for simulation algorithms of Hawkes processes with random marks.
Rate of convergence to equilibrium of marked Hawkes processes / P., Bremaud; Nappo, Giovanna; G. L., Torrisi. - In: JOURNAL OF APPLIED PROBABILITY. - ISSN 0021-9002. - STAMPA. - 39:1(2002), pp. 123-136. [10.1239/jap/1019737993]
Rate of convergence to equilibrium of marked Hawkes processes
NAPPO, Giovanna;
2002
Abstract
In this article we obtain rates of convergence to equilibrium of marked Hawkes processes in two situations. Firstly, the stationary process is the empty process, in which case we speak of the rate of extinction. Secondly, the stationary process is the unique stationary and nontrivial marked Hawkes process, in which case we speak of the rate of installation. The first situation models small epidemics, whereas the results in the second case are useful in deriving stopping rules for simulation algorithms of Hawkes processes with random marks.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.