Averaging dynamics driven by fractional Brownian motion
Probability
2023-03-07 v2
Abstract
We consider slow / fast systems where the slow system is driven by fractional Brownian motion with Hurst parameter . We show that unlike in the case , 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.
Cite
@article{arxiv.1902.11251,
title = {Averaging dynamics driven by fractional Brownian motion},
author = {Martin Hairer and Xue-Mei Li},
journal= {arXiv preprint arXiv:1902.11251},
year = {2023}
}