临界带移民分枝过程的极限行为  

Limit Behaviors for a Critical Galton-Watson Process with Immigration

作　　者：石万林 李豆豆 SHI Wanlin;LI Doudou(College of Mathematics and Physics,North China Electric Power University,Beijing,102206,China;School of Statistics and Data Science,Faculty of Science,Beijing University of Technology,Beijing,100124,China)

机构地区：[1]华北电力大学数理学院,北京102206 [2]北京工业大学理学部统计与数据科学系,北京100124

出　　处：《应用概率统计》2022年第6期919-930,共12页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the National Key R&D Program of China(Grant No.2020YFB1707801);the Fundamental Research Funds for the Central Universities(Grant No.2020MS034);supported by the China Postdoctoral Science Foundation(Grant No.2020M680269);the National Natural Science Foundation of China(Grant No.12101023)。

摘　　要：我们考虑了一个临界带移民的分枝过程Zn,并研究了此过程调和矩的收敛速率,推广了已有文献的结论.证明基于Zn的局部概率估计.作为应用,还得到了SZn:=ZΣn i=1 Xi的大偏差,这里{Xi,i1}是一列独立同分布的随机变量,且X1属于α稳定分布的吸引域(0<α<2).We consider a critical Galton-Watson branching process with immigration Zn,and study the convergence rate of the harmonic moments of this process,improving the results in previous literatures.The proof is based on the local probabilities estimations of Zn.As applications,we obtain the large deviations of SZn:=ZΣn i=1 Xi,where{Xi,i 1}is a sequence of independent and identically distributed random variables,and X1is in the domain of attraction of anα-stable law withα∈(0,2).

关 键 词：调和矩 局部概率 移民 大偏差 

分 类 号：O211.62[理学—概率论与数理统计]