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

Abstract

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

References in corpus (1)

• Well-posedness of the transport equation by stochastic perturbation

Cited by in corpus (2)

• Strong convergence of the Euler--Maruyama approximation for a class of Lévy-driven SDEs
• Regularity properties of jump diffusions with irregular coefficients