| Abstract: |
| Through establishing the regularity estimates for nonlocal Poisson/Stein equations under certain H\older and dissipativity conditions on the coefficients, we derive the $W_d$-convergence rate for the Euler-Maruyama schemes applied to the invariant measure of SDEs driven by $\alpha$-stable noises with $\alpha \in (\frac{1}{2}, 2)$, where $W_d$ denotes the Wasserstein metric corresponding to the distance $d(x,y)=|x-y|^\vartheta \wedge 1$, with $\vartheta \in (0,1] \cap (0,\alpha)$. |
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