Pathwise uniqueness for singular SDEs driven by stable processes

Abstract

We prove pathwise uniqueness for stochastic dierential equations driven by non-degenerate symmetric -stable L evy processes with values in R d having a bounded and -Holder continuous drift term. We assume > 1 = 2 and 2 (1; 2). The proof requires analytic regularity results for the associated integro-dierenti al operators of Kolmogorov type. We also study dierentia- bility of solutions with respect to initial conditions and the homeomorphism property.