Open Access
July 2020 Averaging dynamics driven by fractional Brownian motion
Martin Hairer, Xue-Mei Li
Ann. Probab. 48(4): 1826-1860 (July 2020). DOI: 10.1214/19-AOP1408


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.


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Martin Hairer. Xue-Mei Li. "Averaging dynamics driven by fractional Brownian motion." Ann. Probab. 48 (4) 1826 - 1860, July 2020.


Received: 1 March 2019; Published: July 2020
First available in Project Euclid: 20 July 2020

zbMATH: 07224961
MathSciNet: MR4124526
Digital Object Identifier: 10.1214/19-AOP1408

Primary: 60G22 , 60H05 , 60H10

Keywords: averaging , fractional Brownian motion , sewing lemma , slow/fast system

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 4 • July 2020
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