## Osaka Journal of Mathematics

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

Enrico Priola

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 20 June 2012

https://projecteuclid.org/euclid.ojm/1340197933

Mathematical Reviews number (MathSciNet)
MR2945756

Zentralblatt MATH identifier
1254.60063

#### Citation

Priola, Enrico. Pathwise uniqueness for singular SDEs driven by stable processes. Osaka J. Math. 49 (2012), no. 2, 421--447. https://projecteuclid.org/euclid.ojm/1340197933

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