A projected Euler method for random periodic solutions of semi-linear SDEs with non-globally Lipschitz coefficients

Guo, Yujia and Wang, Xiaojie and Wu, Yue (2024) A projected Euler method for random periodic solutions of semi-linear SDEs with non-globally Lipschitz coefficients. Other. arXiv.org, Ithaca, NY. (https://doi.org/10.48550/arXiv.2406.16089)

[thumbnail of Guo-etal-arXiv-2024-A-projected-Euler-method-for-random-periodic-solutions-of-semi-linear-SDEs]
Preview
 Text. Filename: Guo-etal-arXiv-2024-A-projected-Euler-method-for-random-periodic-solutions-of-semi-linear-SDEs.pdf
Final Published Version
License: Creative Commons Attribution 4.0 logo
Download (368kB)| Preview

Abstract

The present work introduces and investigates an explicit time discretization scheme, called the projected Euler method, to numerically approximate random periodic solutions of semi-linear SDEs under non-globally Lipschitz conditions. The existence of the random periodic solution is demonstrated as the limit of the pull-back of the discretized SDE. Without relying on a priori high-order moment bounds of the numerical approximations, the mean square convergence rate is proved to be order 0.5 for SDEs with multiplicative noise and order 1 for SDEs with additive noise. Numerical examples are also provided to validate our theoretical findings.

CORE (COnnecting REpositories)