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

TL;DR

This paper investigates the weak convergence rate of the Euler-Maruyama scheme for SDEs with H"older continuous drift and multiplicative noise, establishing an almost $(1+ ext{H"older exponent})/2$ rate under certain conditions.

Contribution

It provides a new weak convergence rate result for Euler-Maruyama applied to SDEs with H"older continuous drift, extending previous understanding to this class of equations.

Findings

Weak convergence rate is almost (1 + alpha)/2 for H"older drift

Results apply to SDEs with multiplicative noise and bounded H"older drift

Conditions ensure existence of unique strong solutions

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.