带移民分枝过程的波动极限定理及其统计应用  

A Fluctuation Limit Theorem of Branching Processes with Immigration and Statistical Applications

作　　者：马春华 MA Chunhua(School of Mathematical Sciences and LPMC,Nankai University,300071,China)

机构地区：[1]南开大学数学科学学院和核心数学与组合数学教育部重点实验室,天津300071

出　　处：《应用概率统计》2022年第3期454-474,共21页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the National Natural Science Foundation of China(Grant No.11871032).

摘　　要：我们建立了带移民Galton-Watson分枝过程的波动极限定理,其极限过程为由谱正勒维过程驱动的非时齐Ornstein-Uhlenbeck型过程.作为定理的统计应用,我们得到了后代分布的期望与移民分布的期望的条件最小二乘的渐近估计.We prove a general fluctuation limit theorem for Galton-Watson branching processes with immigration. The limit is a time-inhomogeneous OU type process driven by a spectrally positive Lévy process. As applications of this result, we obtain some asymptotic estimates for the conditional least squares estimators of the means of the offspring and immigration distributions.

关 键 词：带移民Galton-Watson分枝过程 Ornstein-Uhlenbeck型过程 波动极限 条件最小二乘估计 

分 类 号：O211.65[理学—概率论与数理统计]