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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.07298 |
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| _version_ | 1866909948278996992 |
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| author | Bao, Jianhai Hao, Jiaqing Ren, Panpan |
| author_facet | Bao, Jianhai Hao, Jiaqing Ren, Panpan |
| contents | In this paper, we address the issue on non-asymptotic convergence bounds of Euler-type schemes associated with non-dissipative SDEs. On the one hand, for non-degenerate SDEs with super-linear drifts, we propose a novel modified Euler scheme and establish the corresponding non-asymptotic convergence bound under the multiplicative type quasi-Wasserstein distance
by the aid of the asymptotic reflection by coupling. As a direct application of the theory derived, we explore the non-asymptotic convergence bound of the modified tamed/truncated Euler scheme
and, as a byproduct, furnish the associated non-asymptotic convergence rate under the $L^1$-Wasserstein distance although the
dissipativity at infinity is not in force. On the other hand, we tackle the non-asymptotic convergence analysis of the Euler scheme corresponding to a kind of degenerate SDEs, where the underdamped Langevin SDE is a typical candidate. To handle such setting, we also appeal to a carefully tailored coupling approach, where the ingredient in the coupling construction lies in that a proper metric and a suitable substitute in the cut-off function and the reflection matrix need to be chosen appropriately. In addition, as a consequent application, the non-asymptotic convergence bound and the $L^1$-Wasserstein convergence rate are revealed for the kinetic Langevin sampler. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07298 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-asymptotic convergence bounds of modified EM schemes for non-dissipative SDEs Bao, Jianhai Hao, Jiaqing Ren, Panpan Probability In this paper, we address the issue on non-asymptotic convergence bounds of Euler-type schemes associated with non-dissipative SDEs. On the one hand, for non-degenerate SDEs with super-linear drifts, we propose a novel modified Euler scheme and establish the corresponding non-asymptotic convergence bound under the multiplicative type quasi-Wasserstein distance by the aid of the asymptotic reflection by coupling. As a direct application of the theory derived, we explore the non-asymptotic convergence bound of the modified tamed/truncated Euler scheme and, as a byproduct, furnish the associated non-asymptotic convergence rate under the $L^1$-Wasserstein distance although the dissipativity at infinity is not in force. On the other hand, we tackle the non-asymptotic convergence analysis of the Euler scheme corresponding to a kind of degenerate SDEs, where the underdamped Langevin SDE is a typical candidate. To handle such setting, we also appeal to a carefully tailored coupling approach, where the ingredient in the coupling construction lies in that a proper metric and a suitable substitute in the cut-off function and the reflection matrix need to be chosen appropriately. In addition, as a consequent application, the non-asymptotic convergence bound and the $L^1$-Wasserstein convergence rate are revealed for the kinetic Langevin sampler. |
| title | Non-asymptotic convergence bounds of modified EM schemes for non-dissipative SDEs |
| topic | Probability |
| url | https://arxiv.org/abs/2512.07298 |