On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift

@article{Dareiotis2018OnTR,
  title={On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift},
  author={Konstantinos Dareiotis and M'at'e Gerencs'er},
  journal={arXiv: Probability},
  year={2018}
}
The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of $\alpha$-Holder drift in recent literature the rate $\alpha/2$ was proved in many related situations. By exploiting the regularising effect of the noise more efficiently, we show that the rate is in fact arbitrarily close to $1/2$ for all $\alpha>0$. The result extends to Dini continuous coefficients, while in $d=1$ also to a class of everywhere… 
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