带移民Galton-Watson分枝过程溯祖时间的极限理论  

Limit behaviors for coalescence of Galton-Watson processes with immigration

作　　者：姚慧子 王艳萍 晋守博[1] 王悦 YAO Huizi;WANG Yanping;JIN Shoubo;WANG Yue(College of Mathematics and Statistics,Suzhou University,Suzhou 234000,China)

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《湖南文理学院学报(自然科学版)》2025年第2期13-16,共4页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：安徽省高校自然科学研究重大项目(2022AH040207)。

摘　　要：本文研究带移民的Galton-Watson分枝过程溯祖时间的极限分布。考虑带移民的上临界Galton-Watson分枝过程,从第n代的个体中随机挑选2个,往上追溯他们的共同祖先,直到这2个个体在某一代首次聚合成1个个体,称此时的代数为溯祖时间,记作X2n,1,利用已有带移民分枝过程的极限理论来解决溯祖时间的分布以及刻画溯祖时间X2n,1的极限分布。该结果把不带移民的Galton-Watson分枝过程推广到了带移民的情形。This study investigates the limit distribution of the coalescence time of the Galton-Watson branching process with immigration.We consider the supercritical Galton-Watson branching process with immigration,select 2 individuals randomly without replacement from the n-th generation and trace their lines of descent back in time till they coalesce into 1 individual in a certain generation,which is denoted by 2,1,nX and is called the coalescence time.The limit theory of the branching process with immigration is used to address the distribution of the coalescence time and to characterize the limit distribution of the coalescence time.The results extend the Galton-Watson branching process without immigrants to the case of immigrants.

关 键 词：Galton-Watson分枝过程 移民 溯祖时间 极限理论 

分 类 号：O211[理学—概率论与数理统计]