Averaging dynamics driven by fractional Brownian motion

By Martin Hairer, Xue-Mei Li. Annals of Probability, 2019

87 citations recorded by the source corpus.

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 'naively' averaged equation. Our proof strongly relies on the recently obtained stochastic sewing lemma.

Subfields: Economics and Econometrics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9a19a95fc3b565d9998e910ccfe5f435b5426882

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Yong Xu
2. Bin Pei
3. Khoa Le
4. Y. Inahama

In Finance

1. Yong Xu
2. Bin Pei
3. Khoa Le
4. Y. Inahama
5. Lucio Galeati
6. Martin Hairer
7. Xue-Mei Li

In Mathematical Physics

1. Yong Xu
2. Bin Pei
3. Khoa Le
4. Y. Inahama
5. Lucio Galeati
6. Martin Hairer
7. Xue-Mei Li

Citations in the corpus

• Averaging principle for fast-slow system driven by mixed fractional Brownian rough path (2020, background): “It is worth mentioning that Hairer and Li [14] considered a slow-fast system where the slow component is driven by fBm and proved the convergence to the averaged solution takes place in probability.”
• A stochastic sewing lemma and applications (2018, methodology): “After the appearance of the first manuscript of this article, Hairer and Li in [21] have used the stochastic sewing lemma introduced herein to study averaging dynamics of slow and fast systems where the slow system is driven by fractional Brownian motion with Hurst parameter H > 12 .”