2000 character limit reached
Total progeny for spectrally negative branching L{é}vy processes with absorption (2506.04783v1)
Published 5 Jun 2025 in math.PR
Abstract: We consider a spectrally negative branching L{\'e}vy process in which particles are killed upon crossing below zero. It is known that such a process becomes extinct almost surely if the drift toward -$\infty$ is sufficiently strong to counterbalance the reproduction rate. In this note, we study the tail asymptotics of the number of particles absorbed at the boundary during the lifetime of the process, in both the subcritical and critical regimes.