Fundamental solution of kinetic Fokker-Planck operator with anisotropic nonlocal dissipativity

Abstract

By using the probability approach (the Malliavin calculus), we prove the existence of smooth fundamental solutions for degenerate kinetic Fokker-Planck equation with anisotropic nonlocal dissipativity, where the dissipative term is the generator of an anisotropic Lévy process and the drift term is allowed to be cubic growth.

22pp

References in corpus (1)

• Derivative formula and gradient estimate for SDEs driven by $\alpha$-stable processes