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Delay Equations with Non-negativity Constraints Driven by a Hölder Continuous Function of Order $\beta \in\left(\frac{1}{3}, \frac{1}{2}\right)$

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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 $\beta \in\left(\frac{1}{3}, \frac{1}{2}\right)$. 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 $\mathrm{H} \in\left(\frac{1}{3}, \frac{1}{2}\right)$.

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Delay Equations with Non-negativity Constraints Driven by a Hölder Continuous Function of Order $\beta \in\left(\frac{1}{3}, \frac{1}{2}\right)$