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arXiv · 2012.01910

Slow-Fast Systems with Fractional Environment and Dynamics

Xue-Mei Li·Julian Sieber
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Abstract

We prove a fractional averaging principle for interacting slow-fast systems. The mode of convergence is in H\"older norm in probability. The main technical result is a quenched ergodic theorem on the conditioned fractional dynamics. We also establish geometric ergodicity for a class of fractional-driven stochastic differential equations, improving a recent result of Panloup and Richard.

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Xue-Mei Li, Julian Sieber. 2020-12-03. Slow-Fast Systems with Fractional Environment and Dynamics. https://doi.org/10.1214/22-aap1779

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