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arXiv · 2311.01440

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

Fabrice Baudoin·Maria Gordina·David Herzog·Jina Kim·Tai Melcher
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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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Fabrice Baudoin, Maria Gordina, David Herzog, Jina Kim, Tai Melcher. 2023-11-02. Functional inequalities for a family of infinite-dimensional diffusions with degenerate noise. https://arxiv.org/abs/2311.01440

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