Stochastic flow for SDEs with jumps and irregular drift term

We consider non-degenerate SDEs with a $β$-Holder continuous and bounded drift term and driven by a Levy noise $L$ which is of $α$-stable type. If $α\in [1,2)$ and $β\in (1 - \fracα{2},1)$ 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, $α$-stable and symmetric. Here we can also recover relativistic and truncated stable processes and some classes of temperated stable processes.

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