Degenerate Fokker-Planck Equations : Bismut Formula, Gradient Estimate   and Harnack Inequality
  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 $\R^m\times\R^{d}$. The main results are also applied to the study of gradient estimate, entropy/transportation-cost inequality and heat kernel inequalities. 
Arnaud Guillin, Feng-Yu Wang
math.PR