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 $ge$ 1. Namely, we study the case where the
stable index of the driving process Z is $alpha$ = 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 Zt = (Z 1 t ,. .. ,
Z d t) and Z 1 ,. .. , Z d are independent one dimensional Cauchy processes.