A projected Euler Method for Random Periodic Solutions of Semi-linear SDEs with non-globally Lipschitz coefficients
<|reference_start|>A projected Euler Method for Random Periodic Solutions of Semi-linear SDEs with non-globally Lipschitz coefficients: 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.<|reference_end|>
@article{guo2024a,
    title={A projected Euler Method for Random Periodic Solutions of Semi-linear
  SDEs with non-globally Lipschitz coefficients},
    author={Yujia Guo, Xiaojie Wang, Yue Wu},
    journal={arXiv preprint arXiv:2406.16089},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.16089},
    primaryClass={math.NA cs.NA math.PR}
}