Abstract
In this manuscript, we establish local exponential stability of the trivial solution of differential equations driven by Holder continuous paths with Holder 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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