Abstract
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 lead to rate .
Funding Statement
The third author was supported by Alexander von Humboldt Research Fellowship and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 683164).
Acknowledgments
The authors would like to thank the referees for their especially careful reading and many suggestions.
Citation
Konstantinos Dareiotis. Máté Gerencsér. Khoa Lê. "Quantifying a convergence theorem of Gyöngy and Krylov." Ann. Appl. Probab. 33 (3) 2291 - 2323, June 2023. https://doi.org/10.1214/22-AAP1867
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