Gaussian fluctuations for stochastic Volterra equations with small noise

TL;DR

This paper investigates the Gaussian fluctuations of solutions to stochastic Volterra equations with small noise, establishing a central limit theorem and convergence rates using Malliavin calculus, with applications to fractional Brownian motion kernels.

Contribution

It introduces a novel application of Malliavin calculus to derive Gaussian fluctuation results for stochastic Volterra equations with small noise.

Findings

Fluctuation process satisfies a central limit theorem.

Provides optimal convergence rate estimates.

Application demonstrated for equations with fractional Brownian motion kernels.

Abstract

In this paper, we consider a general class of stochastic Volterra equations with small noise. Our aim is to study the fluctuation of the solution around its deterministic limit. We use the techniques of Malliavin calculus to show that the fluctuation process satisfies central limit theorem and provide an optimal estimate for the rate of convergence. An application to stochastic Volterra equations with fractional Brownian motion kernel is given to illustrate the theory.