Randomised Euler-Maruyama Method for SDEs with Hölder Continuous Drift Coefficient Driven by $α$-stable Lévy Process

In this paper, we examine the performance of randomised Euler-Maruyama (EM) method for additive time-inhomogeneous SDEs with an irregular drift driven by symmetric $α$-table process, $α\in (1,2)$. In particular, the drift is assumed to be $β$-Hölder continuous in time and bounded $η$-Hölder continuous in space with $β,η\in (0,1]$. The strong order of convergence of the randomised EM in $L^p$-norm is shown to be $1/2+(β\wedge (η/α)\wedge(1/2))-\varepsilon$ for an arbitrary $\varepsilon\in (0,1/2)$, higher than the one of standard EM, which cannot exceed $β$. The result for the case of $α\in (1,2)$ extends the almost optimal order of convergence of randomised EM obtained in (arXiv:2501.15527) for SDEs driven by Gaussian noise ($α=2$), and coincides with the performance of EM method in simulating time-homogenous SDEs driven by $α$-stable process considered in (arXiv:2208.10052). Various experiments are presented to validate the theoretical performance.