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Regularity properties of jump diffusions with irregular coefficients
Guohuan Zhao · 2018-12-18 · via math.PR updates on arXiv.org

In this paper we investigate the regularity properties of strong solutions to SDEs driven by Lévy 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.

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