Quantifying a convergence theorem of Gyöngy and Krylov
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866917783255646208 |
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| author | Dareiotis, Konstantinos Gerencsér, Máté Lê, Khoa |
| author_facet | Dareiotis, Konstantinos Gerencsér, Máté Lê, Khoa |
| contents | We derive sharp strong convergence rates for the Euler-Maruyama scheme approximating multidimensional SDEs with multiplicative noise without imposing any regularity condition on the drift coefficient. In case the noise is additive, we show that Sobolev regularity can be leveraged to obtain improved rate: drifts with regularity of order $α\in (0,1)$ lead to rate $(1+α)/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_12185 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quantifying a convergence theorem of Gyöngy and Krylov Dareiotis, Konstantinos Gerencsér, Máté Lê, Khoa Probability 60H10, 60H50, 65C30 We derive sharp strong convergence rates for the Euler-Maruyama scheme approximating multidimensional SDEs with multiplicative noise without imposing any regularity condition on the drift coefficient. In case the noise is additive, we show that Sobolev regularity can be leveraged to obtain improved rate: drifts with regularity of order $α\in (0,1)$ lead to rate $(1+α)/2$. |
| title | Quantifying a convergence theorem of Gyöngy and Krylov |
| topic | Probability 60H10, 60H50, 65C30 |
| url | https://arxiv.org/abs/2101.12185 |