Quantifying a convergence theorem of Gyöngy and Krylov

We derive sharp strong convergence rates for the Euler–Maruyama scheme approximating multidimensional SDEs with multiplicative noise without imposing any regularity condition on drift coefficient. In case is additive, we show that Sobolev can be leveraged to obtain improved rate: drifts of order ??(0,1) lead rate (1+?)/2.