Distribution of the largest event in the critical epidemic-type aftershock-sequence model

Abstract

This Brief Report corrects and extends the results of Zhuang and Ogata [Phys. Rev. E 73, 046134 (2006)] on the asymptotic behavior of the largest event in the epidemic-type aftershock-sequence model for earthquake occurrence. We show that, in the special case that the underlying branching process is critical, there exists a previously unnoticed mode of behavior, which occurs when the expected family size grows relatively slowly.