Euler--Maruyama scheme for $\alpha$-stable SDE with distributional drift

In this paper, we consider a class of stochastic differential equations driven by symmetric non-degenerate $\alpha$-stable processes (including cylindrical ones) with $\alpha \in (1,2)$. We first establish a quantitative estimate for the Euler scheme under bounded drift $b(x)$, with an explicit dependence on $\mathrm{\parallel }b{\mathrm{\parallel }}_{L^{\mathrm{\infty }}}$. Then we obtain the weak convergence rates for the case where the drift coefficient belongs to a Besov space of negative order.