Quasi-Invariance for Infinite-Dimensional Kolmogorov Diffusions

We prove Cameron-Martin type quasi-invariance for the heat kernel measure of infinite-dimensional Kolmogorov and similar degenerate diffusions. We first study quantitative functional inequalities, particularly Wang-type Harnack inequalities, for appropriate finite-dimensional approximations of these diffusions, and we prove that these inequalities hold with dimension-independent constants. Applying an approach developed in [ 7 , 12 , 13 ], these uniform bounds may then be used to prove that the heat kernel measure for these infinite-dimensional diffusions is quasi-invariant under changes of the initial state.