Convergence of delay equations driven by a H\"older continuous function of order $\beta\in(\frac13,\frac12)$

Mireia Besalú; Giulia Binotto; Carles Rovira

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arXiv · 2002.07455

Convergence of delay equations driven by a H\"older continuous function of order $\beta\in(\frac13,\frac12)$

Mireia Besalú·Giulia Binotto·Carles Rovira

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Abstract

In this note we show that, when the delay goes to zero, the solution of multidimensional delay differential equations driven by a H\"older continuous function of order $\beta \in (\frac13,\frac12)$ 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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Mireia Besalú, Giulia Binotto, Carles Rovira. 2020-02-18. Convergence of delay equations driven by a H\"older continuous function of order $\beta\in(\frac13,\frac12)$. https://arxiv.org/abs/2002.07455

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