Derivative Formula and Applications for Degenerate Diffusion Semigroups
  By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack inequalities are derived. 
Feng-Yu Wang and Xi-Cheng Zhang
math.PR