Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

TL;DR

This paper establishes existence and uniqueness for multidimensional stochastic delay differential equations with non-negativity constraints driven by fractional Brownian motion, using pathwise Riemann–Stieltjes integrals.

Contribution

It provides the first rigorous proof of existence and uniqueness for such equations driven by fractional Brownian motion with Hurst parameter greater than 1/2.

Findings

Proves existence and uniqueness of solutions

Uses pathwise Riemann–Stieltjes integrals for fractional Brownian motion

Addresses multidimensional stochastic delay equations with reflection

Abstract

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter $H>1/2$. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann--Stieltjes integral.