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 α -Hölder continuous in time and bounded β β -Hölder continuous in space with α ,β ∈ (0,1] α , β ∈ ( 0 , 1 ] . The strong order of convergence of the randomised EM in Lᵖ L p -norm is shown to be 1/2+(α (β /2))-ε 1 / 2 + ( α ∧ ( β / 2 ) ) - ϵ for an arbitrary ε ∈ (0,1/2) ϵ ∈ ( 0 , 1 / 2 ) , higher than the one of standard EM, which is α (1/2+β /2-ε ) 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.