Delay equations with non-negativity constraints driven by a Hölder continuous function of order βin (1/3,1/2)

Abstract

In this note we prove an existence and uniqueness result of solution for multidimensional delay differential equations with normal reflection and driven by a Hölder continuous function of order $\beta \in (\frac{1}{3},\frac{1}{2})$. We also obtain a bound for the supremum norm of this solution. As an application, we get these results for stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H $\in (\frac{1}{3},\frac{1}{2})$.