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).
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)
出处
《应用概率统计》
CSCD
北大核心
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)。
关键词
调和矩
局部概率
移民
大偏差
harmonic moments
local probabilities
immigration
large deviations
