Pathwise uniqueness for singular SDEs driven by stable processes

Understand

We prove pathwise uniqueness for stochastic differential equations driven by non-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 analytic regularity results for associated integro-differential operators of Kolmogorov type.
• We also study differentiability of solutions with respect to initial conditions and the homeomorphism property.