CENTRAL LIMIT THEOREM FOR TEMPORAL AVERAGE OF BACKWARD EULER-MARUYAMA METHOD  

作　　者：Diancong Jin 

机构地区：[1]School of Mathematics and Statistics,Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan 430074,China

出　　处：《Journal of Computational Mathematics》2025年第3期588-614,共27页计算数学(英文)

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.12201228,12171047);by the Fundamental Research Funds for the Central Universities(Grant No.3004011142).

摘　　要：This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem(CLT)of the temporal average of the BEM method,which characterizes its asymptotics in distribution.When the deviation order is smaller than the optimal strong order,we directly derive the CLT of the temporal average through that of original equations and the uniform strong order of the BEM method.For the case that the deviation order equals to the optimal strong order,the CLT is established via the Poisson equation associated with the generator of original equations.Numerical experiments are performed to illustrate the theoretical results.The main contribution of this work is to generalize the existing CLT of the temporal average of numerical methods to that for SODEs with super-linearly growing drift coefficients.

关 键 词：Central limit theorem Temporal average ERGODICITY Backward Euler-Maruyama method 

分 类 号：O211[理学—概率论与数理统计]