Regularity properties of jump diffusions with irregular coefficients

Abstract

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.

28 pages

References in corpus (7)

• A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation
• Strong convergence of the Euler--Maruyama approximation for a class of Lévy-driven SDEs
• Stochastic Lagrangian path for Leray solutions of 3D Navier-Stokes equations
• Well-posedness of supercritical SDE driven by Lévy processes with irregular drifts
• Dirichlet problem for supercritical nonlocal operators
• Nonlocal elliptic equation in Hölder space and the martingale problem
• Uniqueness of solutions of stochastic differential equations