PUB - Publikationen an der Universität Bielefeld

In this paper, we investigate the regularity properties of strong solutions to SDEs driven by Levy processes with irregular drift coefficients. Under some mild conditions, we show that the singular SDE has a unique strong solution for each starting point and the family of all the solutions forms a stochastic flow. Moreover, the Malliavin differentiability of the strong solutions is also obtained. As an application, we also prove a path-by-path uniqueness result for some related random ODEs. Our proofs are based on Schauder's estimate for the corresponding resolvent equation, which is also analytically interesting in itself. (C) 2021 Elsevier Inc. All rights reserved.