Quasi-Invariance for Infinite-Dimensional Kolmogorov Diffusions

Fabrice Baudoin; Maria Gordina; Tai Melcher

doi:10.1007/s11118-023-10070-z

Quasi-Invariance for Infinite-Dimensional Kolmogorov Diffusions

Fabrice Baudoin, Maria Gordina^*, Tai Melcher

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

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Abstract

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.

Originalsprog	Engelsk
Tidsskrift	Potential Analysis
Vol/bind	60
Nummer	2
Sider (fra-til)	807-831
Antal sider	25
ISSN	0926-2601
DOI	https://doi.org/10.1007/s11118-023-10070-z
Status	Udgivet - feb. 2024
Udgivet eksternt	Ja

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title = "Quasi-Invariance for Infinite-Dimensional Kolmogorov Diffusions",

abstract = "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.",

keywords = "Hypoellipticity, Kolmogorov diffusion, Quasi-invariance, Wang{\textquoteright}s Harnack inequality, Primary 60J60, 28C20; Secondary 35H10",

author = "Fabrice Baudoin and Maria Gordina and Tai Melcher",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Nature B.V.",

year = "2024",

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doi = "10.1007/s11118-023-10070-z",

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T1 - Quasi-Invariance for Infinite-Dimensional Kolmogorov Diffusions

AU - Baudoin, Fabrice

AU - Gordina, Maria

AU - Melcher, Tai

PY - 2024/2

Y1 - 2024/2

N2 - 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.

AB - 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.

KW - Hypoellipticity

KW - Kolmogorov diffusion

KW - Quasi-invariance

KW - Wang’s Harnack inequality

KW - Primary 60J60

KW - 28C20; Secondary 35H10

U2 - 10.1007/s11118-023-10070-z

DO - 10.1007/s11118-023-10070-z

M3 - Journal article

AN - SCOPUS:85148871665

SN - 0926-2601

VL - 60

SP - 807

EP - 831

JO - Potential Analysis

JF - Potential Analysis

IS - 2

ER -

Quasi-Invariance for Infinite-Dimensional Kolmogorov Diffusions

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