On the regularisation of the noise for the euler-maruyama scheme with irregular drift

Abstract

The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of α-Hölder drift in the recent literature the rate α/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 α > 0. The result extends to Dini continuous coefficients, while in d = 1 also to all bounded measurable coefficients.