Heat kernel and gradient estimates for kinetic SDEs with low regularity coefficients

TL;DR

This paper derives heat kernel and gradient estimates for the density of kinetic degenerate Kolmogorov SDEs under minimal assumptions ensuring weak well-posedness.

Contribution

It provides new heat kernel and gradient estimates for kinetic SDEs with low regularity coefficients, extending existing results to more general conditions.

Findings

Established heat kernel estimates for kinetic SDEs.

Derived gradient bounds under minimal regularity assumptions.

Ensured well-posedness of the SDEs under the considered conditions.

Abstract

We establish heat kernel and gradient estimates for the density of kinetic degenerate Kolmogorov stochastic differentia equations. Our results are established under somehow minimal assumptions that guarantee the SDE is weakly well posed.