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

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

2011-03-14

arxiv.org/abs/1103.2817v3

Mathematics

Probability

23 pages

Scientific paper

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.

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