On the weak rate of convergence for the Euler–Maruyama scheme with Hölder drift

Abstract

We consider stochastic differential equations with bounded α-Hölder continuous drift, with α∈(0,1), driven by multiplicative noise. We moreover assume that the diffusion coefficient is uniformly elliptic and bounded, with bounded first and second order partial derivatives. We show that the weak rate of convergence for the Euler–Maruyama scheme is arbitrarily close to (1+α)/2.