Pathwise uniqueness for singular SDEs driven by stable processes

Details Pathwise uniqueness for singular SDEs driven by stable processes Pathwise uniqueness for singular SDEs driven by stable processes

2010-05-23

arxiv.org/abs/1005.4237v2

Mathematics

Dynamical Systems

The main change is the new statement (iii) in Theorem 1.1 about differentiability of solutions with respect to initial conditi

Scientific paper

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.

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