Stochastic Volterra equations driven by fractional Brownian motion with Hurst parameter H > 1/2

TL;DR

This paper establishes existence, uniqueness, and finite moments for solutions to stochastic Volterra equations driven by fractional Brownian motion with Hurst parameter greater than 1/2, using pathwise Riemann-Stieltjes integrals.

Contribution

It provides a novel existence and uniqueness result for stochastic Volterra equations driven by fractional Brownian motion with H > 1/2, employing pathwise integrals.

Findings

Solutions have finite moments.

Unique solutions exist under specified conditions.

The approach uses pathwise Riemann-Stieltjes integrals.

Abstract

In this note we prove an existence and uniqueness result of solution for stochastic Volterra integral equations driven by a fractional Brownian motion with Hurst parameter H > 1/2, showing also that the solution has finite moments. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann-Stieltjes integral.