Using synchronous coupling, the authors prove reverse Bakry-Emery estimates, reverse Poincare and logarithmic Sobolev inequalities, Wang-Harnack inequality, and a Liouville property for Kolmogorov-type hypoelliptic diffusions.
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Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
Using synchronous coupling, the authors prove reverse Bakry-Emery estimates, reverse Poincare and logarithmic Sobolev inequalities, Wang-Harnack inequality, and a Liouville property for Kolmogorov-type hypoelliptic diffusions.