Randomised Euler-Maruyama method for SDEs with Hölder continuous drift coefficient
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866913666726625280 |
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| author | Bao, Jianhai Wu, Yue |
| author_facet | Bao, Jianhai Wu, Yue |
| contents | In this paper, we examine the performance of randomised Euler-Maruyama (EM) method for additive time-inhomogeneous SDEs with an irregular drift. In particular, the drift is assumed to be $α$-Hölder continuous in time and bounded $β$-Hölder continuous in space with $α,β\in (0,1]$. The strong order of convergence of the randomised EM in $L^p$-norm is shown to be $1/2+(α\wedge (β/2))-ε$ for an arbitrary $ε\in (0,1/2)$, higher than the one of standard EM, which is $α\wedge (1/2+β/2-ε)$. The proofs highly rely on the stochastic sewing lemma, where we also provide an alternative proof when handling time irregularity for a comparison. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15527 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Randomised Euler-Maruyama method for SDEs with Hölder continuous drift coefficient Bao, Jianhai Wu, Yue Probability Numerical Analysis 65C30, 65C05, 60H10, 60H35, 60L90 In this paper, we examine the performance of randomised Euler-Maruyama (EM) method for additive time-inhomogeneous SDEs with an irregular drift. In particular, the drift is assumed to be $α$-Hölder continuous in time and bounded $β$-Hölder continuous in space with $α,β\in (0,1]$. The strong order of convergence of the randomised EM in $L^p$-norm is shown to be $1/2+(α\wedge (β/2))-ε$ for an arbitrary $ε\in (0,1/2)$, higher than the one of standard EM, which is $α\wedge (1/2+β/2-ε)$. The proofs highly rely on the stochastic sewing lemma, where we also provide an alternative proof when handling time irregularity for a comparison. |
| title | Randomised Euler-Maruyama method for SDEs with Hölder continuous drift coefficient |
| topic | Probability Numerical Analysis 65C30, 65C05, 60H10, 60H35, 60L90 |
| url | https://arxiv.org/abs/2501.15527 |