Uniform Cramer moderate deviations and Berry-Esseen bounds for a supercritical branching process in a random environment
作者机构：Center for Applied MathematicsTianjin UniversityTianjin 300072China School of Mathematics and StatisticsNortheastern University at QinhuangdaoQinhuangdao 066004China Universite de Bretagne-SudLMBAUMR CNRS 6205Campus de Tohannic56017 VannesFrance School of Statistics and MathematicsZhongnan University of Economics and LawWuhan 430073China
出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)
年 卷 期：2020年第15卷第5期
页 面：891-914页
核心收录：
基 金：supported by the National Natural Science Foundation of China(Grant Nos.11601375,11971063,11731012) the Natural ScienceFoundation of Guangdong Province(Grant No.2018A030313954) the Centre Henri Lebesgue(CHL,ANR-11-LABX-0020-01).
主 题：Branching processes random environment Cramer moderatedeviations Berry-Esseen bounds
摘 要：Let{Zn,n≥0}be a supercritical branching process in an independent and identically distributed random environment.We prove Cramer moderate deviations and Berry-Esseen bounds for log(Zn+n0/Zn0)uniformly in n0∈N,which extend the corresponding results by I.Grama,Q.Liu,and M.Miqueu[Stochastic Process.Appl.,2017,127:1255-1281]established for n0=0.The extension is interesting in theory,and is motivated by applications.A new method is developed for the proofs;some conditions of Grama et al.are relaxed in our present setting.An example of application is given in constructing confidence intervals to estimate the criticality parameter in terms of log(Zn+n0/Zn0)and n.
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