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arXiv · 1005.4237

Pathwise uniqueness for singular SDEs driven by stable processes

Enrico Priola
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Abstract

We prove pathwise uniqueness for stochastic differential equations driven by non-degenerate symmetric $α$-stable Lévy processes with values in $\R^d$ having a bounded and $β$-Hölder continuous drift term. We assume $β> 1 - \fracα{2} $ and $α\in [ 1, 2)$. 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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Enrico Priola. 2010-06-02. Pathwise uniqueness for singular SDEs driven by stable processes. https://arxiv.org/abs/1005.4237

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