School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China.
Chaos. 2022 Dec;32(12):123135. doi: 10.1063/5.0131433.
This paper focuses on the averaging principle of Caputo fractional stochastic differential equations (SDEs) with multiplicative fractional Brownian motion (fBm), where Hurst parameter 1/2<H<1 and the integral of fBm as a generalized Riemann-Stieltjes integral. Under suitable assumptions, the averaging principle on Hölder continuous space is established by giving the estimate of Hölder norm. Specifically, we show that the solution of the original fractional SDEs converges to the solution of the proposed averaged fractional SDEs in the mean square sense and gives an example to illustrate our result.
本文研究了具有乘性分数布朗运动（fBm）的 Caputo 分数随机微分方程（SDE）的平均原理，其中 Hurst 参数 1/2<H<1，fBm 的积分作为广义黎曼-斯蒂尔杰斯积分。在适当的假设下，通过给出 Hölder 范数的估计，在 Hölder 连续空间中建立了平均原理。具体来说，我们证明了原分数 SDE 的解在均方意义下收敛到所提出的平均分数 SDE 的解，并给出了一个例子来说明我们的结果。
