November 2023 Averaging principles for mixed fast-slow systems driven by fractional Brownian motion
Bin Pei, Yuzuru Inahama, Yong Xu
Author Affiliations +
Kyoto J. Math. 63(4): 721-748 (November 2023). DOI: 10.1215/21562261-2023-0001


We focus on fast-slow systems involving both fractional Brownian motion (fBm) and standard Brownian motion (Bm). The integral with respect to Bm is the standard Itô integral, and the integral with respect to fBm is a generalized Riemann–Stieltjes integral by means of fractional calculus. We establish an averaging principle in which the fast-varying diffusion process of the fast-slow systems acts as a “noise” to be averaged out in the limit. We show that the slow process has a limit in the mean square sense, which is characterized by the solution of stochastic differential equations driven by fBm whose coefficients are averaged with respect to the stationary measure of the fast-varying diffusion. An implication is that one can ignore the complex original systems and concentrate on the averaged systems instead. This averaging principle paves the way for reduction of computational complexity.


Download Citation

Bin Pei. Yuzuru Inahama. Yong Xu. "Averaging principles for mixed fast-slow systems driven by fractional Brownian motion." Kyoto J. Math. 63 (4) 721 - 748, November 2023.


Received: 28 February 2021; Revised: 25 August 2021; Accepted: 25 October 2021; Published: November 2023
First available in Project Euclid: 18 September 2023

MathSciNet: MR4643002
Digital Object Identifier: 10.1215/21562261-2023-0001

Primary: 60G22
Secondary: 34C29 , 60H10

Keywords: averaging principles , Fast-slow systems , fractional Brownian motion , generalized Riemann–Stieltjes integral , standard Brownian motion

Rights: Copyright © 2023 by Kyoto University


This article is only available to subscribers.
It is not available for individual sale.

Vol.63 • No. 4 • November 2023
Back to Top