A simple method for the existence of a density for stochastic evolutions with rough coefficients

TL;DR

This paper extends a simple method to prove the existence and regularity of densities for solutions of stochastic differential equations, even with rough coefficients and summable drifts, improving understanding of their probabilistic behavior.

Contribution

It generalizes a previous method to cover local density estimates, existence with less regular drifts, and enhanced regularity results for stochastic evolutions.

Findings

Established local density estimates for stochastic differential equations.

Proved existence of densities with summable drifts.

Improved regularity results for the densities of stochastic evolutions.

Abstract

We extend the validity of a simple method for the existence of a density for stochastic differential equations, first introduced in [DebRom2014], by proving local estimate for the density, existence for the density with summable drift, and by improving the regularity of the density.