Averaging dynamics driven by fractional Brownian motion

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.