Three Regimes of the Distribution of the Largest Event in the Critical ETAS Model.

This article proves that three regimes of asymptotic behavior exist in the critical case and transit smoothly from one to another according to a single parameter. Our results correct and extend the results of Saichev and Sornette (2005), Zhuang and Ogata (2006), and Vere-Jones and Zhuang (2008) on the asymptotic behavior of the largest event in the epidemic-type aftershock sequence model for earthquake occurrence when the process is critical. [ABSTRACT FROM AUTHOR]