$W_{\bf d}$-convergence rate of EM schemes for invariant measures of supercritical stable SDEs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916482169962496 |
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| author | Chen, Peng Xu, Lihu Zhang, Xiaolong Zhang, Xicheng |
| author_facet | Chen, Peng Xu, Lihu Zhang, Xiaolong Zhang, Xicheng |
| contents | By establishing the regularity estimates for nonlocal Stein/Poisson equations under $γ$-order Hölder and dissipative conditions on the coefficients, we derive the $W_{\bf d}$-convergence rate for the Euler-Maruyama schemes applied to the invariant measure of SDEs driven by multiplicative $α$-stable noises with $α\in (\frac{1}{2}, 2)$, where $W_{\bf d}$ denotes the Wasserstein metric with ${\bf d}(x,y)=|x-y|^γ\wedge 1$ and $γ\in ((1-α)_+, 1]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09949 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $W_{\bf d}$-convergence rate of EM schemes for invariant measures of supercritical stable SDEs Chen, Peng Xu, Lihu Zhang, Xiaolong Zhang, Xicheng Probability 60H10 By establishing the regularity estimates for nonlocal Stein/Poisson equations under $γ$-order Hölder and dissipative conditions on the coefficients, we derive the $W_{\bf d}$-convergence rate for the Euler-Maruyama schemes applied to the invariant measure of SDEs driven by multiplicative $α$-stable noises with $α\in (\frac{1}{2}, 2)$, where $W_{\bf d}$ denotes the Wasserstein metric with ${\bf d}(x,y)=|x-y|^γ\wedge 1$ and $γ\in ((1-α)_+, 1]$. |
| title | $W_{\bf d}$-convergence rate of EM schemes for invariant measures of supercritical stable SDEs |
| topic | Probability 60H10 |
| url | https://arxiv.org/abs/2411.09949 |