Large Deviations for a Critical Galton-Watson Branching Process  

作　　者：Dou-dou LI Wan-lin SHI Mei ZHANG 

机构地区：[1]College of Statistics and Data Science,Faculty of Science,Beijing University of Technology,Beijing 100124,China [2]Department of Mathematics and Physics,North China Electric Power University,Beijing 102206,China [3]Laboratory of Mathematics and Complex Systems(Ministry of Education),School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China

出　　处：《Acta Mathematicae Applicatae Sinica》2025年第2期456-478,共23页应用数学学报(英文版)

基　　金：supported by the National Natural Science Foundation of China(No.12101023,No.11871103 and 12271043);the National Key Research and Development Program of China(No.2020YFA0712900);Fundamental Research Funds for the Central Universities(No.2023MS077)).

摘　　要：In this paper,a critical Galton-Watson branching process {Z_(n)} is considered.Large deviation rates of SZ_(n):=Σ_(i=1)^_(Z_(n)) Xi are obtained,where {X_(i);i≥1} is a sequence of independent and identically distributed random variables and X_(1) is in the domain of attraction of an-stable law with α∈(0,2).One shall see that the convergence rate is determined by the tail index of X_(1) and the variance of Z_(1).Our results can be compared with those ones of the supercritical case.

关 键 词：large deviation branching process CRITICAL α-stable 

分 类 号：O211[理学—概率论与数理统计]