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

We are interested in the Euler-Maruyama dicretization of the formal SDE, $dX_t=b(t,X_t)dt+dZ_t$, where $Z$ is a symmetric isotropic d dimensional stable process of index $α\in (1,2)$, 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.

💡 Research Summary

This paper investigates the weak error on the probability densities generated by the Euler–Maruyama discretisation of a stochastic differential equation (SDE) driven by a symmetric isotropic α‑stable Lévy process with index α∈(1,2). The drift coefficient b(t,x) is allowed to be distributional: it belongs to a mixed Lebesgue–Besov space L^r(