Martingale problems for some degenerate Kolmogorov equations

TL;DR

This paper establishes Calderón-Zygmund estimates and well-posedness results for degenerate Kolmogorov equations, ensuring uniqueness in law for related stochastic differential equations and providing density estimates.

Contribution

It introduces new Calderón-Zygmund estimates for degenerate equations and proves well-posedness and uniqueness for associated martingale problems.

Findings

Calderón-Zygmund estimates for degenerate equations

Well-posedness of the martingale problem

Density estimates for solutions

Abstract

We obtain Calder{\'o}n-Zygmund estimates for some degenerate equations of Kolmogorov type with inhomogeneous coefficients. We then derive the well-posedness of the martingale problem associated to related degenerate operators, and therefore uniqueness in law for the corresponding stochastic differential equations. Some density estimates are established as well.