**Abstract:** | Studies of time series data suggest that the increments of the data are often correlated, and its variance evolve like a power function. In this joint work with Martin Hairer, we consider a slow / fast systems where the slow system is driven by fractional Brownian motion with Hurst parameter greater or equal to 1/2. We show that the convergence to the averaged solution is unlike the deterministic case. Although we have to rely on the stochasticity in the fractional noise, both the mode of convergence and the averaging mechanics are different from the diffusion case. Our proof strongly relies on the recently obtained stochastic sewing lemma. |