Averaging dynamics driven by fractional Brownian motion
Abstract
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 'na\"ively' averaged equation. Our proof strongly relies on the recently obtained stochastic sewing lemma.
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