@article{72a27ac36ba94f5d8cad74200a23f29a,
title = "Asymptotic expansion for branching killed Brownian motion with drift",
abstract = "Let Z(0,∞) t be the point process formed by the positions of all particles alive at time t in a branching Brownian motion with drift −θ and killed upon reaching 0. We assume θ ∈ [0,√2) and study the asymptotic expansions of Zt(0,∞) (A) for intervals A ⊂ (0, ∞) under the assumption that (Formula Presented) for some large λ. These results extend and sharpen the results of Louidor and Saglietti [J. Stat. Phys, 2020] and that of Kesten [Stochastic Process. Appl., 1978].",
keywords = "asymptotic expansion, branching Brownian motion with absorption, martingale approximation, spine decomposition",
author = "Haojie Hou and Ren, {Yan Xia} and Renming Song",
note = "The research of this project is supported by the National Key R&D Program of China (No. 2020YFA0712900). Haojie Hou\u2019s research is partially supported by the China Postdoctoral Science Foundation (No. 2024M764112). Yan-Xia Ren\u2019s research is partially supported by NSFC (Grant Nos. 12071011 and 12231002) and The Fundamental Research Funds for Central Universities, Peking University LMEQF. Renming Song\u2019s research is partially supported by the Simons Foundation (#960480, Renming Song). Part of the research for this paper was done while the third-named author was visiting Jiangsu Normal University, where he was partially supported by a grant from the National Natural Science Foundation of China (11931004, Yingchao Xie) and by the Priority Academic Program Development of Jiangsu Higher Education Institutions.",
year = "2025",
doi = "10.1214/25-EJP1289",
language = "English (US)",
volume = "30",
journal = "Electronic Journal of Probability",
issn = "1083-6489",
publisher = "Institute of Mathematical Statistics",
}