Stochastic flow for SDEs with jumps and irregular drift term. (English) Zbl 1322.60095
Chojnowska-Michalik, Anna (ed.) et al., Stochastic analysis. Special volume in honour of Jerzy Zabczyk. Selected papers based on the presentations at the Banach Center conference on stochastic analysis and control, Bȩdlewo, Poland, May 6–10, 2013. Warsaw: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-28-7/pbk). Banach Center Publications 105, 193-210 (2015).
Summary: 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 [E. Priola, Osaka J. Math. 49, No. 2, 421–447 (2012; Zbl 1254.60063)], 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.
For the entire collection see [Zbl 1323.60004].
For the entire collection see [Zbl 1323.60004].
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60J75 | Jump processes (MSC2010) |
| 60G51 | Processes with independent increments; Lévy processes |
| 60G52 | Stable stochastic processes |
| 34F05 | Ordinary differential equations and systems with randomness |
| 35B65 | Smoothness and regularity of solutions to PDEs |
