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 . The main results are also applied to the study of gradient estimate, entropy/transportation-cost inequality and heat kernel inequalities. [Copyright &y& Elsevier]