\({\mathcal{W}}\)\({}_{\textrm{d}}\)-Convergence Rate of EM Schemes for Invariant Measures of Supercritical Stable SDEs

Abstract. By establishing the regularity estimates for nonlocal Stein/Poisson equations under [Formula: see text]-order Hölder and dissipative conditions on the coefficients, we derive the [Formula: see text][Formula: see text]-convergence rate for the Euler–Maruyama schemes applied to the invariant measure of SDEs driven by multiplicative [Formula: see text]-stable noises with [Formula: see text], where [Formula: see text][Formula: see text] denotes the Wasserstein metric with [Formula: see text][Formula: see text] and [Formula: see text].