We consider slow/fast systems where the slow system is driven by fractional Brownian motion with Hurst parameter H>1/2. We show that unlike in the case H=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.
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Hairer et al. (2020) studied this question.
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