Weak Error on the densities for the Euler scheme of stable additive SDEs with Besov drift

Abstract

We are interested in the Euler-Maruyama dicretization of the formal SDE, $d{X}_t=b(t,X_t)dt+d{Z}_t$, where $Z$ is a symmetric isotropic d dimensional stable process of index $\alpha \in (1,2)$, and $b$ is distributional. It belongs to a mix Lebesgue-Besov space. The associated parameters satisfy some constraints which guarantee weak-well posedness. Defining an appropriate Euler scheme, we obtain a convergence rate for the weak error on the densities. The rate depends on the parameters.