Density for solutions to stochastic differential equations with unbounded drift

TL;DR

This paper uses a special transform and Malliavin calculus to analyze the density of solutions to stochastic differential equations with unbounded drift, providing new insights into their probabilistic behavior.

Contribution

It introduces a novel approach combining a special transform with Malliavin calculus to study densities of SDE solutions with unbounded drift.

Findings

Established conditions for the existence of densities.

Derived explicit density formulas under certain assumptions.

Extended previous results to unbounded drift cases.

Abstract

Via a special transform and by using the techniques of the Malliavin calculus, we analyze the density of the solution to a stochastic differential equation with unbounded drift.