Fractional White Noise Perturbations of Parabolic Volterra Equations

TL;DR

This paper extends existing results on fractional white noise perturbations of parabolic Volterra equations, showing that solution regularity improves with higher Hurst parameters.

Contribution

It generalizes prior work by analyzing the effect of fractional white noise with Hurst parameter 0<H<1 on Volterra equations, revealing increased regularity.

Findings

Solution regularity increases with Hurst parameter H

Similar results to previous studies are obtained for fractional noise

The work broadens understanding of stochastic Volterra equations with fractional noise

Abstract

Aim of this work is to extend the results of Cl\'ement, Da Prato & Pr\"uss on the fractional white noise perturbation with Hurst parameter 0<H<1. We will obtain similar results and it will turn out that the regularity of the solution u(t) of the stochastic Volterra equation increases with Hurst parameter H.