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Central Limit Theorem for Temporal Average of Backward Euler-Maruyama Method

Central Limit Theorem for Temporal Average of Backward Euler-Maruyama Method

Year:    2025

Author:    Diancong Jin

Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 588–614

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2311-m2023-0147

Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 588–614

Published online:    2025-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Central limit theorem Temporal average Ergodicity Backward Euler-Maruyama method.

Author Details

Diancong Jin