$W_{\mathbf{d}}$-convergence rate of EM schemes for invariant measures of supercritical stable SDEs

Abstract

By establishing the regularity estimates for nonlocal Stein/Poisson equations under $\gamma$-order Hölder and dissipative conditions on the coefficients, we derive the $W_{\mathbf{d}}$-convergence rate for the Euler-Maruyama schemes applied to the invariant measure of SDEs driven by multiplicative $\alpha$-stable noises with $\alpha \in (\frac{1}{2},2)$, where $W_{\mathbf{d}}$ denotes the Wasserstein metric with $\mathbf{d}(x,y)=|x-y{|}^{\gamma }\wedge 1$ and $\gamma \in ((1-\alpha {)}_{+},1]$.

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