Averaging dynamics driven by fractional Brownian motion

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 ‘na"ively’ averaged equation. Our proof strongly relies on the recently obtained stochastic sewing lemma.