Abstract
We consider a spectrally negative branching Lévy process where the particles undergo dyadic branching and are killed when entering the negative half-line. 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.
Acknowledgments
We are grateful to the referee whose very careful reading and suggestions help to improve the presentation of the paper.
Citation
Christophe Profeta. "Survival and maximum of spectrally negative branching Lévy processes with absorption." Electron. Commun. Probab. 29 1 - 15, 2024. https://doi.org/10.1214/24-ECP627
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