Functional Stochastic Differential Equations with Positivity Constraints Driven by Fractional Brownian Motion

TL;DR

This paper investigates reflected stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter greater than 1/2, proving existence and convergence of solutions under specific conditions.

Contribution

It introduces a new approach to solving reflected fractional stochastic differential equations and establishes convergence of the Euler method for these equations.

Findings

Existence of solutions proved for the equations

Convergence of the Euler method established

Uniqueness shown under constant argument deviation condition

Abstract

This paper studies a stochastic functional differential equation driven by a fractional Brownian motion with Hurst parameter H>1/2, constrained to be reflected at 0. We prove the existence of solutions using the Euler method. However, uniqueness is demonstrated only under the condition that the fractional term exhibits constant argument deviation. Additionally, we establish the convergence of the method.