Abstract
We consider slow/fast systems where the slow system is driven by fractional Brownian motion with Hurst parameter $H>{\frac{1}{2}}$. We show that unlike in the case $H={\frac{1}{2}}$, convergence to the averaged solution takes place in probability and the limiting process solves the ‘naïvely’ averaged equation. Our proof strongly relies on the recently obtained stochastic sewing lemma.
Citation
Martin Hairer. Xue-Mei Li. "Averaging dynamics driven by fractional Brownian motion." Ann. Probab. 48 (4) 1826 - 1860, July 2020. https://doi.org/10.1214/19-AOP1408
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