TY - JOUR
T1 - Central Limit Theorem for Temporal Average of Backward Euler-Maruyama Method
AU - Jin , Diancong
JO - Journal of Computational Mathematics
VL - 3
SP - 588
EP - 614
PY - 2024
DA - 2024/11
SN - 43
DO - http://doi.org/10.4208/jcm.2311-m2023-0147
UR - https://global-sci.org/intro/article_detail/jcm/23551.html
KW - Central limit theorem, Temporal average, Ergodicity, Backward Euler-Maruyama method.
AB - <p style="text-align: justify;">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.</p>