Gradient Bounds for Kolmogorov Type Diffusions

TL;DR

This paper investigates gradient bounds and functional inequalities for Kolmogorov type diffusions using coupling and generalized Gamma calculus methods, comparing their effectiveness and limitations.

Contribution

It provides a comparative analysis of coupling and Gamma calculus techniques for deriving gradient bounds in Kolmogorov diffusions.

Findings

Coupling methods offer intuitive probabilistic bounds.

Gamma calculus provides analytical inequalities.

Both methods have unique advantages and limitations.

Abstract

We study gradient bounds and other functional inequalities for the diffusion semigroup generated by Kolmogorov type operators. The focus is on two different methods: coupling techniques and generalized $\Gamma$-calculus techniques. The advantages and drawbacks of each of these methods are discussed.