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 ...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.展开更多
In this paper,we establish normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for SDE.Due to our results,Berry-Esseen's bounds and moderate deviation principles are a...In this paper,we establish normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for SDE.Due to our results,Berry-Esseen's bounds and moderate deviation principles are also obtained.Our normalized Cramér-type moderate deviations refine the recent work of Lu et al.(2022).展开更多
A Berry–Esseen bound is obtained for self-normalized martingales under the assumption of finite moments.The bound coincides with the classical Berry–Esseenboundforstandardizedmartingales.Anexampleisgiventoshowtheopt...A Berry–Esseen bound is obtained for self-normalized martingales under the assumption of finite moments.The bound coincides with the classical Berry–Esseenboundforstandardizedmartingales.Anexampleisgiventoshowtheoptimality of the bound.Applications to Student’s statistic and autoregressive process are also discussed.展开更多
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).
文摘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.
基金supported by National Natural Science Foundation of China(Grant No.11971063)。
文摘In this paper,we establish normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for SDE.Due to our results,Berry-Esseen's bounds and moderate deviation principles are also obtained.Our normalized Cramér-type moderate deviations refine the recent work of Lu et al.(2022).
文摘A Berry–Esseen bound is obtained for self-normalized martingales under the assumption of finite moments.The bound coincides with the classical Berry–Esseenboundforstandardizedmartingales.Anexampleisgiventoshowtheoptimality of the bound.Applications to Student’s statistic and autoregressive process are also discussed.
