Averaging dynamics driven by fractional Brownian motion. (English) Zbl 1453.60087

Summary: 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.


60G22 Fractional processes, including fractional Brownian motion
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H05 Stochastic integrals
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