Wasserstein-1 Distance and Nonuniform Berry-Esseen Bound for a Supercritical Branching Process in a Random Environment  

作　　者：Hao WU Xiequan FAN Zhiqiang GAO Yinna YE 

机构地区：[1]Center for Applied Mathematics,Tianjin University,Tianjin 300072,P.R.China [2]School of Mathematics and Statistics,Northeastern University at Qinhuangdao,Hebei 066004,P.R.China [3]Laboratory of Mathematics and Complex Systems,School of Mathematical Sciences,Beijing Normal University,Beijing 100875,P.R.China [4]Department of Applied Mathematics,School of Mathematics and Physics,Xi'an Jiaotong-Liverpool University,Jiangsu 215123,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2023年第6期737-753,共17页数学研究及应用(英文版)

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)。

摘　　要：Let(Z_(n))_(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(Z_(n))_(n)≥0,which completes a result of Grama et al.[Stochastic Process.Appl.,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.

关 键 词：Branching processes Random environment Wasserstein-1 distance Nonuniform Berry-Esseen bounds MR(2020)Subject Classification 60J80 60K37 60F05 62E20 

分 类 号：O211.65[理学—概率论与数理统计]