A projected Euler Method for Random Periodic Solutions of Semi-linear SDEs with non-globally Lipschitz coefficients
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912130847997952 |
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| author | Guo, Yujia Wang, Xiaojie Wu, Yue |
| author_facet | Guo, Yujia Wang, Xiaojie Wu, Yue |
| contents | 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 of the approximation scheme 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16089 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A projected Euler Method for Random Periodic Solutions of Semi-linear SDEs with non-globally Lipschitz coefficients Guo, Yujia Wang, Xiaojie Wu, Yue Numerical Analysis Probability 37H99, 60H10, 60H35, 65C30 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 of the approximation scheme 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. |
| title | A projected Euler Method for Random Periodic Solutions of Semi-linear SDEs with non-globally Lipschitz coefficients |
| topic | Numerical Analysis Probability 37H99, 60H10, 60H35, 65C30 |
| url | https://arxiv.org/abs/2406.16089 |