Total progeny for spectrally negative branching Lévy processes with absorption
Résumé
We consider a spectrally negative branching Lévy 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 -∞ 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.
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