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 $H>\frac{1}{2}$. 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.

References in corpus (3)

• Formulae for the derivatives of heat semigroups
• An averaging principle for a completely integrable stochastic Hamiltonian system
• A stochastic sewing lemma and applications

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• Concentration estimates for SPDEs driven by fractional Brownian motion
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