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Asymptotical Stability of Differential Equations Driven by Hölder Continuous Paths

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Abstract

In this manuscript, we establish local exponential stability of the trivial solution of differential equations driven by Hölder continuous paths with Hölder exponent greater than 1/2. This applies in particular to stochastic differential equations driven by fractional Brownian motion with Hurst parameter greater than 1/2. We motivate the study of local stability by giving a particular example of a scalar equation, where global stability of the trivial solution can be obtained.

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Authors and Affiliations

  1. Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080, Sevilla, Spain

    María J. Garrido-Atienza

  2. Institut für Mathematik, Universität Mannheim, A5, 6, 68131, Mannheim, Germany

    Andreas Neuenkirch

  3. Institut für Stochastik, Friedrich Schiller Universität Jena, Ernst Abbe Platz 2, 77043, Jena, Germany

    Björn Schmalfuß

Authors
  1. María J. Garrido-Atienza
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  2. Andreas Neuenkirch
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  3. Björn Schmalfuß
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Corresponding author

Correspondence to María J. Garrido-Atienza.

Additional information

This work was partially supported by MTM2015-63723-P, MINECO/FEDER funding (M. J. Garrido-Atienza and B. Schmalfuß).

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Garrido-Atienza, M.J., Neuenkirch, A. & Schmalfuß, B. Asymptotical Stability of Differential Equations Driven by Hölder Continuous Paths. J Dyn Diff Equat 30, 359–377 (2018). https://doi.org/10.1007/s10884-017-9574-6

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  • DOI: https://doi.org/10.1007/s10884-017-9574-6

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