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In this paper we introduce a new technique to construct unique strongsolutions of SDEs with singular coefficients driven by certain Levy processes.Our method which is based on Malliavin calculus does not rely on a pathwiseuniqueness argument. Furthermore, the approach, which provides a directconstruction principle, grants the additional insight that the obtainedsolutions are Malliavin differentiable.

On the Construction and Malliavin Differentiability of Levy Noise Driven SDEs with Singular Coefficients