Normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for the SDE  

作　　者：Xiequan Fan Haijuan Hu Lihu Xu 

机构地区：[1]Center for Applied Mathematics,Tianjin University,Tianjin 300072,China [2]School of Mathematics and Statistics,Northeastern University at Qinhuangdao,Qinhuangdao 066004,China [3]Department of Mathematics,Faculty of Science and Technology,University of Macao,Macao,China

出　　处：《Science China Mathematics》2024年第8期1865-1880,共16页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11971063)。

摘　　要：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).

关 键 词：Euler-Maruyama scheme Cramer-type moderate deviations self-normalized sequences Berry-Esseen’s bounds 

分 类 号：O211.63[理学—概率论与数理统计]