Weak uniqueness for SDEs driven by supercritical stable processes with Holder drifts

Abstract: In this paper, we investigate stochastic differential equations(SDEs) driven by a class of supercritical $\alpha$-stable process(including the rotational symmetric $\alpha-$stable process) with drift $b$. The weak well-posedness is proved, provided that the $(1-\alpha)$-H\"older semi-norm of $b$ is sufficient small.