Publikation: Sample Paths Estimates for Stochastic Fast-Slow Systems Driven by Fractional Brownian Motion
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2020
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Journal of Statistical Physics. Springer Science+Business Media B.V.. 2020, 179(5-6), pp. 1222-1266. ISSN 0022-4715. eISSN 1572-9613. Available under: doi: 10.1007/s10955-020-02485-4
Zusammenfassung
We analyze the effect of additive fractional noise with Hurst parameter 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.
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510 Mathematik
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Fast-slow systems, Fractional Brownian motion, Sample path estimates, Correlated noise, AMOC model
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EICHINGER, Katharina, Christian KUEHN, Alexandra BLESSING-NEAMTU, 2020. Sample Paths Estimates for Stochastic Fast-Slow Systems Driven by Fractional Brownian Motion. In: Journal of Statistical Physics. Springer Science+Business Media B.V.. 2020, 179(5-6), pp. 1222-1266. ISSN 0022-4715. eISSN 1572-9613. Available under: doi: 10.1007/s10955-020-02485-4BibTex
@article{Eichinger2020-06Sampl-53769,
year={2020},
doi={10.1007/s10955-020-02485-4},
title={Sample Paths Estimates for Stochastic Fast-Slow Systems Driven by Fractional Brownian Motion},
number={5-6},
volume={179},
issn={0022-4715},
journal={Journal of Statistical Physics},
pages={1222--1266},
author={Eichinger, Katharina and Kuehn, Christian and Blessing-Neamtu, Alexandra}
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<dcterms:abstract xml:lang="eng">We analyze the effect of additive fractional noise with Hurst parameter 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.</dcterms:abstract>
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