Order-one explicit approximations of random periodic solutions of semi-linear SDEs with multiplicative noise
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912175991291904 |
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| author | Guo, Yujia Wang, Xiaojie Wu, Yue |
| author_facet | Guo, Yujia Wang, Xiaojie Wu, Yue |
| contents | This paper is devoted to order-one explicit approximations of random periodic solutions to multiplicative noise driven stochastic differential equations (SDEs) with non-globally Lipschitz coefficients. The existence of the random periodic solution is demonstrated as the limit of the pull-back of the discretized SDE. A novel approach is introduced to analyze mean-square error bounds of the proposed scheme that does not depend on a prior high-order moment bounds of the numerical approximations. Under mild assumptions, the proposed scheme is proved to achieve an expected order-one mean square convergence in the infinite time horizon. Numerical examples are finally provided to verify the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Order-one explicit approximations of random periodic solutions of semi-linear SDEs with multiplicative noise Guo, Yujia Wang, Xiaojie Wu, Yue Probability Numerical Analysis 37H99, 60H10, 60H35, 65C30 This paper is devoted to order-one explicit approximations of random periodic solutions to multiplicative noise driven stochastic differential equations (SDEs) with non-globally Lipschitz coefficients. The existence of the random periodic solution is demonstrated as the limit of the pull-back of the discretized SDE. A novel approach is introduced to analyze mean-square error bounds of the proposed scheme that does not depend on a prior high-order moment bounds of the numerical approximations. Under mild assumptions, the proposed scheme is proved to achieve an expected order-one mean square convergence in the infinite time horizon. Numerical examples are finally provided to verify the theoretical results. |
| title | Order-one explicit approximations of random periodic solutions of semi-linear SDEs with multiplicative noise |
| topic | Probability Numerical Analysis 37H99, 60H10, 60H35, 65C30 |
| url | https://arxiv.org/abs/2501.01474 |