Osaka Journal of Mathematics

Pathwise uniqueness for singular SDEs driven by stable processes

Enrico Priola

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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.

Article information

Osaka J. Math., Volume 49, Number 2 (2012), 421-447.

First available in Project Euclid: 20 June 2012

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Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 34F05: Equations and systems with randomness [See also 34K50, 60H10, 93E03]
Secondary: 60J75: Jump processes 35B65: Smoothness and regularity of solutions


Priola, Enrico. Pathwise uniqueness for singular SDEs driven by stable processes. Osaka J. Math. 49 (2012), no. 2, 421--447.

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