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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.03104 |
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| _version_ | 1866910929304682496 |
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| author | Li, Xiang Mo, Yingjun Yang, Haoran |
| author_facet | Li, Xiang Mo, Yingjun Yang, Haoran |
| contents | Consider the following stochastic differential equation driven by multiplicative noise on $\mathbb{R}^d$ with a superlinearly growing drift coefficient, \begin{align*}
\mathrm{d} X_t = b (X_t) \, \mathrm{d} t + σ(X_t) \, \mathrm{d} B_t. \end{align*} It is known that the corresponding explicit Euler schemes may not converge. In this article, we analyze an explicit and easily implementable numerical method for approximating such a stochastic differential equation, i.e. its tamed Euler-Maruyama approximation. Under partial dissipation conditions ensuring the ergodicity, we obtain the uniform-in-time convergence rates of the tamed Euler-Maruyama process under $L^{1}$-Wasserstein distance and total variation distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03104 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tamed Euler-Maruyama method for SDEs with non-globally Lipschitz drift and multiplicative noise Li, Xiang Mo, Yingjun Yang, Haoran Probability Consider the following stochastic differential equation driven by multiplicative noise on $\mathbb{R}^d$ with a superlinearly growing drift coefficient, \begin{align*} \mathrm{d} X_t = b (X_t) \, \mathrm{d} t + σ(X_t) \, \mathrm{d} B_t. \end{align*} It is known that the corresponding explicit Euler schemes may not converge. In this article, we analyze an explicit and easily implementable numerical method for approximating such a stochastic differential equation, i.e. its tamed Euler-Maruyama approximation. Under partial dissipation conditions ensuring the ergodicity, we obtain the uniform-in-time convergence rates of the tamed Euler-Maruyama process under $L^{1}$-Wasserstein distance and total variation distance. |
| title | Tamed Euler-Maruyama method for SDEs with non-globally Lipschitz drift and multiplicative noise |
| topic | Probability |
| url | https://arxiv.org/abs/2505.03104 |