Randomised Euler-Maruyama method for SDEs with Hölder continuous drift coefficient

In this paper, we examine the performance of randomised Euler-Maruyama (EM) method for additive time-inhomogeneous SDEs with an irregular drift. In particular, the drift is assumed to be α-Hölder continuous in time and bounded β-Hölder continuous in space with α,β∈(0,1]. The strong order of convergence of the randomised EM in Lp-norm is shown to be 1/2+(α∧(β/2))−ϵ for an arbitrary ϵ∈(0,1/2), higher than the one of standard EM, which is α∧(1/2+β/2−ϵ). The proofs highly rely on the stochastic sewing lemma, where we also provide an alternative proof when handling time irregularity for a comparison.