BERRY-ESSEEN TYPE INEQUALITY FOR A POISSON RANDOMLY INDEXED BRANCHING PROCESS VIA STEIN'S METHOD

被引：6
作者：
Gao, Zhenlong [1 ]
机构：
[1] Qufu Normal Univ, Sch Stat, Qufu 273165, Peoples R China
来源：
JOURNAL OF MATHEMATICAL INEQUALITIES | 2018年 / 12卷 / 02期
关键词：
Berry-Esseen's inequality; Stein's method; randomly indexed branching process; MODERATE DEVIATIONS;
D O I：
10.7153/jmi-2018-1243
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A Beny-Esseen type inequality is proved via Stein's method for the logarithm of a Poisson randomly indexed branching process {Z(Nt)}, where {Z(n)} is a supercritical Galton-Watson process and {N-t} is a Poisson process which is independent of {Z(n)}.
引用
收藏
页码：573 / 582
页数：10
相关论文
共 17 条
[1]  
Athreya K., 1972, BRANCHING PROCESS
[2]  
CHEN L. H. Y., NORMAL APPROXIMATION
[3]   Stock prices as branching processes in random environments: Estimation [J].
Dion, JP ;
Epps, TW .
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 1999, 28 (04) :957-975
[4]  
EPPS T., 1996, Commun. Statist. Stoch. Models, V12, P529
[5]   Large and moderate deviations for a renewal randomly indexed branching process [J].
Gao, Zhenlong ;
Wang, Weigang .
STATISTICS & PROBABILITY LETTERS, 2016, 116 :139-145
[6]   LIMIT THEOREMS FOR A SUPERCRITICAL POISSON RANDOM INDEXED BRANCHING PROCESS [J].
Gao, Zhenlong ;
Zhang, Yanhua .
JOURNAL OF APPLIED PROBABILITY, 2016, 53 (01) :307-314
[7]   Large deviations for a Poisson random indexed branching process [J].
Gao, Zhenlong ;
Wang, Weigang .
STATISTICS & PROBABILITY LETTERS, 2015, 105 :143-148
[8]   Large and moderate deviations for a class of renewal random indexed branching process [J].
Gao, Zhenlong ;
Zhang, Yanhua .
STATISTICS & PROBABILITY LETTERS, 2015, 103 :1-5
[9]   Berry Esseen's bound and Cramer's large deviation expansion for a supercritical branching process in a random environment [J].
Grama, Ion ;
Liu, Quansheng ;
Miqueu, Eric .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2017, 127 (04) :1255-1281
[10]   AN LP BOUND FOR REMAINDER IN A COMBINATORIAL CENTRAL LIMIT-THEOREM [J].
HO, ST ;
CHEN, LHY .
ANNALS OF PROBABILITY, 1978, 6 (02) :231-249
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