Convergence rate of numerical scheme for SDEs with a distributional drift in Besov space

This paper is concerned with numerical solutions of one-dimensional SDEs with the drift being a generalised function in the spatial variable, in particular being a ½-Hölder continuous function of time taking values in a Hölder-Zygmund space C−γ of negative order −γ < 0. We design an Euler– Maruyama numerical scheme and prove its convergence, obtaining an upper bound for the strong L1 convergence rate. We finally implement the scheme and discuss the results obtained.