Degenerate Fokker-Planck Equations : Bismut Formula, Gradient Estimate and Harnack Inequality

Abstract

By constructing successful couplings for degenerate diffusion processes, explicit derivative formula and Harnack type inequalities are presented for solutions to a class of degenerate Fokker-Planck equations on ${\mathbb{R}}^m\times {\mathbb{R}}^d$. The main results are also applied to the study of gradient estimate, entropy/transportation-cost inequality and heat kernel inequalities.

23 pages

References in corpus (2)

• Formulae for the derivatives of heat semigroups
• Harnack inequality and applications for stochastic generalized porous media equations

Cited by in corpus (2)

• Derivative Formula and Applications for Degenerate Diffusion Semigroups
• Bismut Formulae and Applications for Functional SPDEs