We consider non-degenerate SDEs with a β-Hölder continuous and bounded drift term and driven by a Lévy noise L which is of α-stable type. If β > 1 - α/2 and α ∈ [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, α-stable and symmetric. Here we can also recover relativistic and truncated stable processes and some classes of tempered stable processes.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc105-0-12,
author = {Enrico Priola},
title = {Stochastic flow for SDEs with jumps and irregular drift term},
journal = {Banach Center Publications},
volume = {104},
year = {2015},
pages = {193-210},
zbl = {1322.60095},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc105-0-12}
}
Enrico Priola. Stochastic flow for SDEs with jumps and irregular drift term. Banach Center Publications, Tome 104 (2015) pp. 193-210. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc105-0-12/