Using synchronous coupling, the authors prove reverse Bakry-Emery estimates, reverse Poincare and logarithmic Sobolev inequalities, Wang-Harnack inequality, and a Liouville property for Kolmogorov-type hypoelliptic diffusions.
Functional inequalities for a family of infinite-dimensional diffusions with degenerate noise
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
fields
math.PR 1years
2024 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
Using synchronous coupling, the authors prove reverse Bakry-Emery estimates, reverse Poincare and logarithmic Sobolev inequalities, Wang-Harnack inequality, and a Liouville property for Kolmogorov-type hypoelliptic diffusions.