Abstract
We prove pathwise uniqueness for stochastic differential equations driven by non-degenerate symmetric $\alpha$-stable Lévy processes with values in $\mathbb{R}^{d}$ having a bounded and $\beta$-Hölder continuous drift term. We assume $\beta > 1 - \alpha/2$ and $\alpha \in [1, 2)$. The proof requires analytic regularity results for the associated integro-differential operators of Kolmogorov type. We also study differentiability of solutions with respect to initial conditions and the homeomorphism property.
Citation
Enrico Priola. "Pathwise uniqueness for singular SDEs driven by stable processes." Osaka J. Math. 49 (2) 421 - 447, June 2012.
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