Functional stochastic differential equations with positivity constraints driven by fractional Brownian motion

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. We have proved uniqueness only for a special case of this type of equation, as well as the convergence of the Euler scheme.