Euler--Maruyama scheme for $\hat{I}\pm$-stable SDE with distributional drift

Abstract

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

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