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Functional inequalities for a family of infinite-dimensional diffusions with degenerate noise

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arxiv 2311.01440 v1 pith:YTJQLVJL submitted 2023-11-02 math.PR

Fabrice Baudoin , Maria Gordina , David Herzog , Jina Kim , Tai Melcher This is my paper · ORCID
classification math.PR
keywords degeneratediffusionsfamilyfunctionalgammainequalitiesinfinite-dimensionalnoise
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abstract

For a family of infinite-dimensional diffusions with degenerate noise, we develop a modified $\Gamma$ 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 $\Gamma$ 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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