Regularity of density for SDEs driven by degenerate Lévy noises

Abstract

By using Bismut's approach about the Malliavin calculus with jumps, we study the regularity of the distributional density for SDEs driven by degenerate additive Lévy noises. Under full Hörmander's conditions, we prove the existence of distributional density and the weak continuity in the first variable of the distributional density. Under the uniform first order Lie's bracket condition, we also prove the smoothness of the density.

25 pages

References in corpus (5)

• Densities for SDEs driven by degenerate $\alpha$-stable processes
• Nonlocal Hormander's hypoellipticity theorem
• Strong Feller properties for degenerate SDEs with jumps
• Fundamental solution of kinetic Fokker-Planck operator with anisotropic nonlocal dissipativity
• Smooth densities of stochastic differential equations forced by degenerate stable type noises

Cited by in corpus (3)

• Fundamental solutions of nonlocal Hörmander's operators
• Smooth densities of stochastic differential equations forced by degenerate stable type noises
• Fokker-Planck equations for Marcus stochastic differential equations driven by Levy processes