随机环境下两个上临界分支过程的参数比较  

Comparison on the Criticality Parameters for Two Supercritical Branching Processes in Random Environments

作　　者：范协铨 胡海娟 吴浩 叶印娜 Fan Xiequan;Hu Haijuan;Wu Hao;Ye Yinna(School of Mathematics and Statistics,Northeastern University at Qinhuangdao,Hebei Qinhuangdao 066003;Center for Applied Mathematics,Tianjin University,Tianjin 300072;School of Mathematics and Physics,Xi'an Jiaotong-Liverpool University,Jiangsu Suzhou 215123)

机构地区：[1]东北大学秦皇岛分校数学与统计学院,河北秦皇岛066003 [2]天津大学应用数学中心,天津300072 [3]西交利物浦大学数学物理学院,江苏苏州215123

出　　处：《数学物理学报（A辑）》2023年第5期1440-1470,共31页Acta Mathematica Scientia

基　　金：国家自然科学基金(11971063)。

摘　　要：设(Z_(1,n))_(n≥0)和(Z_(2,n))_(n≥0)是两个在独立同分布随机环境下的上临界分支过程,并且其关键参数分别为μ1和μ2.容易知道,在适当条件下,1/nlnZ_(1,n)和1/mlnZ_(2,m)分别依概率收敛到μ1和μ2.该文旨在讨论两个上临界分支过程的关键参数之差μ1−μ2的估计问题,它可以被看作是一类双样本U统计量问题.我们得到了1/nlnZ_(1,n−1/m)lnZ_(2,m)的中心极限定理,非一致性Berry-Esseen估计和Cramér型中偏差.最后,作为应用部分,指出了以上的结果可用于关键参数置信区间的构造.Let{Z_(1,n),n≥0}and{Z_(2,n),n≥0}be two supercritical branching processes in different random environments,with criticality parametersμ1 andμ2 respectively.It is known that with certain conditions,1/nlnZ_(1,n)→μ1 and 1/mlnZ_(2,m)→μ2 in probability as m,n→∞.In this paper,we are interested in the comparison on the two criticality parameters,which can be regarded as two-sample U-statistic.To this end,we prove a non-uniform Berry-Esseen's bound and Cramér's moderate deviations for 1/nlnZ_(1,n)−1/mlnZ_(2,m) as m,n→∞.An application is also given for constructing confidence intervals ofμ1−μ2.

关 键 词：分支过程 随机环境 Berry-Esseen 估计 Cramér 型中偏差 

分 类 号：O211.65[理学—概率论与数理统计]