Existence and Besov regularity of the density for a class of SDEs with Volterra noise

TL;DR

This paper proves the existence and Besov regularity of the density for solutions to SDEs driven by Gaussian Volterra processes using fractional integration by parts, under weak regularity conditions on the drift.

Contribution

It introduces a simple fractional integration by parts method to establish density regularity for SDEs with Volterra noise, broadening applicability with weak drift assumptions.

Findings

Proves existence of density for SDE solutions with Volterra noise.

Establishes Besov regularity of the density.

Applies method to various Gaussian Volterra noises.

Abstract

By using a simple method based on the fractional integration by parts, we prove the existence and the Besov regularity of the density for solutions to stochastic differential equations driven by an additive Gaussian Volterra process. We assume weak regularity conditions on the drift. Several examples of Gaussian Volterra noises are discussed.