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

Fabrice Baudoin; Maria Gordina; David Herzog; Jina Kim; Tai Melcher

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

Fabrice Baudoin, Maria Gordina, David Herzog, Jina Kim, Tai Melcher

Institut for Matematik

Publikation: Working paper/Preprint › Preprint

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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.

Originalsprog	Udefineret/Ukendt
Status	Udgivet - 2 nov. 2023

Emneord

math.PR
Primary 60J60, 28C20, Secondary 35H10

Adgang til dokumentet

2311.01440v1

Citationsformater

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