Convergence of delay equations driven by a Hölder continuous function of order 1/3<β<1/2.

Abstract

In this article we show that, when the delay approaches zero, the solution of multidimensional delay differential equations driven by a Hölder continuous function of order 1/3 < \beta < 1/2 converges with the supremum norm to the solution for the equation without delay. Finally we discuss the applications to stochastic differential equations.