Weak well-posedness and weak discretization error for stable-driven SDEs with Lebesgue drift

Abstract

We are interested in the discretization of stable driven SDEs with additive noise for $\hat{I}\pm$ $\in$ (1, 2) and Lq -- Lp drift under the Serrin type condition $\hat{I}\pm$/q + d/p < $\hat{I}\pm$ -- 1. We show weak existence and uniqueness as well as heat kernel estimates for the SDE and obtain a convergence rate of order (1/$\hat{I}\pm$)*($\hat{I}\pm$ -- 1 -- $\hat{I}\pm$/q - d/p) for the difference of the densities for the Euler scheme approximation involving suitably cutoffed and time randomized drifts.