Publishing house / Banach Center Publications / All volumes

Abstract

We consider non-degenerate SDEs with a $\beta$-Hölder continuous and bounded drift term and driven by a Lévy noise $L$ which is of $\alpha$-stable type. If $\beta > 1 - \frac{\alpha}{2} $ and $\alpha \in [1,2)$, we show pathwise uniqueness and existence of a stochastic flow. We follow the approach of [Priola, Osaka J. Math. 2012] improving the assumptions on the noise $L$. In our previous paper $L$ was assumed to be non-degenerate, $\alpha$-stable and symmetric. Here we can also recover relativistic and truncated stable processes and some classes of tempered stable processes.