Abstract
We prove a fractional averaging principle for interacting slow-fast systems. The mode of convergence is in Hölder 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.
Funding Statement
Partial support from the EPSRC under grant no. EP/S023925/1 is also acknowledged.
Acknowledgments
We would like to thank the anonymous referees for their careful reading and helpful comments.
Citation
Xue-Mei Li. Julian Sieber. "Slow-fast systems with fractional environment and dynamics." Ann. Appl. Probab. 32 (5) 3964 - 4003, October 2022. https://doi.org/10.1214/22-AAP1779
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