Weak well-posedness of multidimensional stable driven SDEs in the critical case.

We establish weak well-posedness for critical symmetric stable driven SDEs in ℝ d with additive noise Z , d ≥ 1. Namely, we study the case where the stable index of the driving process Z is α = 1 which exactly corresponds to the order of the drift term having the coefficient b which is continuous and bounded. In particular, we cover the cylindrical case when Z t = (Z t 1 , ... , Z t d) and Z 1 , ... , Z d are independent one-dimensional Cauchy processes. Our approach relies on L p -estimates for stable operators and uses perturbative arguments. [ABSTRACT FROM AUTHOR]