Abstract
AbstractWe analyze the effect of additive fractional noise with Hurst parameter $$H > {1}/{2}$$
H
>
1
/
2
on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet, the setting of fractional Brownian motion does not allow us to use the martingale methods from fast-slow systems with Brownian motion. We thoroughly investigate the case where the deterministic system permits a uniformly hyperbolic stable slow manifold. In this setting, we provide a neighborhood, tailored to the fast-slow structure of the system, that contains the process with high probability. We prove this assertion by providing exponential error estimates on the probability that the system leaves this neighborhood. We also illustrate our results in an example arising in climate modeling, where time-correlated noise processes have become of greater relevance recently.
Funder
Volkswagen Foundation
Deutsche Forschungsgemeinschaft
H2020 European Research Council
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
6 articles.
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