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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.

MSC:

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