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

2020/02/18 by Mireia Besalú, Besalú, Mireia, Giulia Binotto +3
Computer Science · Mathematics · #60H05 #60H07 #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Matrix Theory and Algorithms #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2002.07455

openalex publication_date 2020/02/18 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

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∈ (\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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