随机环境中带移民分枝过程的Cramér大偏差展式  

Cramer's Large Deviation Expansion for a Supercritical Branching Process with Immigration in a Random Environment

作　　者：王艳清[1] 刘全升 范协铨 Yan Qing WANG;Quan Sheng LIU;Xie Quan FAN(School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,P.R.China;LMBA,Universite de Bretagne-Sud,Campus de Tohannic,Vannes 56017,France;Center for Applied Mathematics,Tianjin 300072,P.R.China)

机构地区：[1]中南财经政法大学统计与数学学院,武汉430073 [2]法国南布列塔尼大学,瓦讷56017 [3]天津大学应用数学中心,天津300072

出　　处：《数学学报（中文版）》2022年第5期877-890,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(11731012);中央高校基本科研业务费(2722021AJ014,2722021BX023)。

摘　　要：本文考虑独立同分布的随机环境中带移民的分枝过程(Z_(n)).基于(Z_(n))的结构,利用测度变换技巧,并借助随机游动的相关结果,我们得到关于logZ_(n)的Cramer型大偏差展式.Let(Z_(n))be a supercritical branching process with immigration in an independent and identically distributed random environment.Based on the structure of Z_(n),using related results on random walks and technique of measure change,we establish a Cramer's large deviation expansion for log Z_(n).

关 键 词：分枝过程 随机环境 Cramer型大偏差展式 

分 类 号：O211[理学—概率论与数理统计]