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Stochastic flow for SDEs with jumps and irregular drift term

Volume 105 / 2015

Enrico Priola Banach Center Publications 105 (2015), 193-210 MSC: 60H10, 35B65, 60J75, 34F05. DOI: 10.4064/bc105-0-12

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.

Authors

  • Enrico PriolaDipartimento di Matematica “Giuseppe Peano”
    Università di Torino
    via Carlo Alberto 10
    10123 Torino, Italy
    e-mail

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