Precise Asymptotics in Limit Theorems for a Supercritical Branching Process with Immigration in a Random Environment  

作　　者：Chun Mao HUANG Rui ZHANG Zhi Qiang GAO 

机构地区：[1]Department of Mathematics,Harbin Institute of Technology(Weihai),Weihai 264209,P.R.China [2]School of Mathematical Sciences,Beijing Normal University,Beijing 100875,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第8期1850-1874,共25页数学学报（英文版）

基　　金：Supported by Shandong Provincial Natural Science Foundation(Grant No.ZR2021MA085);National Natural Science Foundation of China(Grant No.11971063)。

摘　　要：Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit theorem on log Zn and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm.By similar approach and with the help of a change of measure,we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.

关 键 词：Branching process with immigration random environment central limit theorem large deviation 

分 类 号：O211.65[理学—概率论与数理统计]