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

TL;DR

This paper investigates stochastic differential equations constrained to non-negative values, driven by fractional Brownian motion with Hurst parameter greater than 1/2, using Young integral techniques for pathwise solutions.

Contribution

It introduces a novel approach to solving non-negativity constrained SDEs driven by fractional Brownian motion using Young integrals.

Findings

Established existence of solutions for the integral equation.

Applied the integral results to solve the stochastic differential equations.

Provided a pathwise solution framework for fractional Brownian motion-driven SDEs.

Abstract

In this paper we consider stochastic differential equations with non-negativity constraints, driven by a fractional Brownian motion with Hurst parameter $H>\1/2$. We first study an ordinary integral equation where the integral is defined in the Young sense and then we apply this result pathwise to solve the stochastic problem.