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

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.