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...

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Bibliographic Details
Published inPotential analysis Vol. 60; no. 2; pp. 807 - 831
Main Authors Baudoin, Fabrice, Gordina, Maria, Melcher, Tai
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.02.2024
Springer Nature B.V
Subjects
Functional Analysis
Geometry
Inequalities
Invariance
Mathematics
Mathematics and Statistics
Potential Theory
Probability Theory and Stochastic Processes
Quasi-invariance
Hypoellipticity
Kolmogorov diffusion
Primary 60J60
Wang’s Harnack inequality
28C20; Secondary 35H10
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Summary: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.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-023-10070-z