Survival and maximum of spectrally negative branching L{é}vy processes with absorption
arXiv:2306.00383
Abstract
We consider a spectrally negative branching L{é}vy process where the particles undergo dyadic branching and are killed when entering the negative half-plane. The purpose of this short note is to give conditions under which this process dies out a.s., and then study the asymptotics of its all-time maximum.