@article{3892f4816799427bb08b7561586d0296,
title = "Invariance principle for the maximal position process of branching Brownian motion in random environment",
abstract = "In this paper we study the maximal position process of branching Brownian motion in random spatial environment. The random environment is given by a process (formula presented) satisfying certain conditions. We show that the maximum position Mt of particles alive at time t satisfies a quenched strong law of large numbers and an annealed invariance principle.",
keywords = "branching Brownian motion, invariance principle, law of large numbers, random environment",
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). Yan-Xia Ren{\textquoteright}s research is partially supported by NSFC (Grant Nos. 11731009, 12071011 and 12231002) and LMEQF. Renming Song{\textquoteright}s research is partially supported by the Simons Foundation (#960480, Renming Song). †Yan-Xia Ren is the corresponding author. ‡School of Mathematical Sciences, Peking University, Beijing, 100871, P.R. China. E-mail: houhaojie@pku. edu.cn §LMAM School of Mathematical Sciences & Center for Statistical Science, Peking University, Beijing, 100871, P.R. China. E-mail:
[email protected] ¶Department of Mathematics, University of Illinois, Urbana, IL 61801, U.S.A. E-mail:
[email protected] We thank the referee for helpful comments and suggestions on the first version of this paper. 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 = "2023",
doi = "10.1214/23-ejp956",
language = "English (US)",
volume = "28",
journal = "Electronic Journal of Probability",
issn = "1083-6489",
publisher = "Institute of Mathematical Statistics",
}