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We prove pathwise uniqueness for stochastic differential equations driven bynon-degenerate symmetric $\alpha$-stable L\'evy processes with values in $\R^d$having a bounded and $\beta$-H\"older continuous drift term. We assume $\beta >1 - \frac{\alpha}{2} $ and $\alpha \in [ 1, 2)$. The proof requires analyticregularity results for associated integro-differential operators of Kolmogorovtype. We also study differentiability of solutions with respect to initialconditions and the homeomorphism property.

Pathwise uniqueness for singular SDEs driven by stable processes