Wasserstein-1 Distance and Nonuniform Berry-Esseen Bound for a Supercritical Branching Process in a Random Environment
作者机构：Center for Applied Mathematics Tianjin University School of Mathematics and Statistics Northeastern University at Qinhuangdao Laboratory of Mathematics and Complex Systems School of Mathematical SciencesBeijing Normal University Department of Applied Mathematics School of Mathematics and PhysicsXi'an Jiaotong-Liverpool University
出 版 物：《Journal of Mathematical Research with Applications》 (数学研究及应用(英文))
年 卷 期：2023年第43卷第6期
页 面：737-753页
核心收录：
学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学]
基 金：Supported by the National Natural Science Foundation of China (Grant No. 11971063) CY Initiative of Excellence (Grant No.“Investissements d’Avenir” ANR-16-IDEX-0008) Project “EcoDep”(Grant No. PSI-AAP2020-0000000013)
主 题：Branching processes Random environment Wasserstein-1 distance Nonuniform Berry-Esseen bounds
摘 要：Let(Zn)n≥0be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-1 distance for the process(Zn)n≥0, which completes a result of Grama et al. [Stochastic ***., 2017, 127(4): 1255–1281]. Moreover, an exponential nonuniform Berry-Esseen bound is also given. At last, some applications of the main results to the confidence interval estimation for the criticality parameter and the population size Znare discussed.
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