Euler–Maruyama scheme for α-stable SDE with distributional drift

Abstract

In this paper, we consider a class of stochastic differential equations driven by symmetric non-degenerate α -stable processes (including cylindrical ones) with 𝛼 ∈ ( 1 , 2 ) . We first establish a quantitative estimate for the Euler scheme under smooth bounded drift 𝑏 ⁡ ( 𝑥 ) , with polynomial dependence on ‖ 𝑏 ‖ ∞ . Then we obtain the weak convergence rates for the case where the drift coefficient belongs to a Besov space of negative order.