Convergence of delay equations driven by a Hölder continuous function of order $β\in(\frac13,\frac12)$

In this note we show that, when the delay goes to zero, the solution of multidimensional delay differential equations driven by a Hölder continuous function of order $β\in (\frac13,\frac12)$ converges with the supremum norm to the solution for the equation without delay. As an application, we discuss the applications to stochastic differential equations.

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