2023/10/08 by Fan Yang, Yang, Fan, Yaping Zhu +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2310.04976
openalex publication_date 2023/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 random shifted decorated Poisson point process. Furthermore, we show that the law of the right-most particle converges to the law of a random shifted Gumbel random variable.