The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of $\alpha $-Hölder drift in the 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 all bounded measurable coefficients.
"On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift." Electron. J. Probab. 25 1 - 18, 2020. https://doi.org/10.1214/20-EJP479