A note on the weak rate of convergence for the Euler-Maruyama scheme with H\"older drift

Abstract

We consider SDEs with bounded and $\alpha$-H\"older continuous drift, with $\alpha \in (0,1)$, driven by multiplicative noise. We show that under sufficient conditions on the diffusion matrix, which guarantee the existence of a unique strong solution, the weak rate of convergence for the Euler-Maruyama scheme is almost $(1+\alpha)/2$. The present paper forms part of the author's master's thesis.