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arXiv · 1604.06213

Asymptotical stability of differential equations driven by H\"older--continuous paths

María J. Garrido-Atienza·Andreas Neuenkirch·Björn Schmalfuß
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Abstract

In this manuscript, we establish asymptotic local exponential stability of the trivial solution of differential equations driven by H\"older--continuous paths with H\"older 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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María J. Garrido-Atienza, Andreas Neuenkirch, Björn Schmalfuß. 2016-04-21. Asymptotical stability of differential equations driven by H\"older--continuous paths. https://arxiv.org/abs/1604.06213

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