Functional inequalities for a family of infinite-dimensional diffusions with degenerate noise
Abstract
For a family of infinite-dimensional diffusions with degenerate noise, we develop a modified calculus on finite-dimensional projections of the equation in order to produce explicit functional inequalities that can be scaled to infinite dimensions. The choice of our operator appears canonical in our context, as the estimates depend only on the induced control distance. We apply the general analysis to a number of examples, exploring implications for quasi-invariance and uniqueness of stationary distributions.
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