Abstract
In this paper, we study branching Brownian motion with absorption, in which particles undergo Brownian motions with drift and are killed upon reaching the origin. We prove that the extremal process of this branching Brownian motion with absorption converges to a randomly shifted decorated Poisson point process. Furthermore, we show that the law of the right-most particle converges to the law of a randomly shifted Gumbel random variable.
Funding Statement
The research of this project is supported by the National Key R&D Program of China (No. 2020YFA0712900). The research of F. Yang is supported by China Postdoctoral Science Foundation (No. 2023TQ0033) and Postdoctoral Fellowship Program of CPSF (No. GZB20230068).
Acknowledgments
We would like to express deep gratitude to Professor Yanxia Ren and Professor Renming Song for their constructive suggestions. We also thank the referee for the careful reading of the first version of this paper and for very helpful comments for improving the quality of the paper.
Citation
Fan Yang. Yaping Zhu. "The extremal process of branching Brownian motion with absorption." Electron. J. Probab. 29 1 - 21, 2024. https://doi.org/10.1214/24-EJP1213
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