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Averaging dynamics driven by fractional Brownian motion (1902.11251v2)
Published 28 Feb 2019 in math.PR
Abstract: We consider slow / fast systems where the slow system is driven by fractional Brownian motion with Hurst parameter $H>{1\over 2}$. We show that unlike in the case $H={1\over 2}$, convergence to the averaged solution takes place in probability and the limiting process solves the 'na\"ively' averaged equation. Our proof strongly relies on the recently obtained stochastic sewing lemma.