Density estimates for solutions to one dimensional Backward SDE's

TL;DR

This paper establishes conditions under which solutions to one-dimensional backward stochastic differential equations have densities with Gaussian bounds, enhancing understanding of their probabilistic behavior.

Contribution

It provides new sufficient conditions ensuring the existence of densities with Gaussian estimates for solutions to general backward SDEs.

Findings

Solutions have densities with Gaussian bounds under specified conditions.

Upper and lower Gaussian estimates are derived for these densities.

The results apply to a broad class of backward SDEs.

Abstract

In this paper, we derive sufficient conditions for each component of the solution to a general backward stochastic differential equation to have a density for which upper and lower Gaussian estimates can be obtained.