Averaging principle for fast-slow system driven by mixed fractional Brownian rough path

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:301

Article

Pei, Bin^1,2  Inahama, Yuzuru²  Xu, Yong¹ 

[1] Northwestern Polytech Univ, Sch Math & Stat, 127 West Youyi Rd, Xian 710072, Shaanxi, Peoples R China

[2] Kyushu Univ, Fac Math, Nishi Ku, 744 Motooka, Fukuoka 8190395, Japan

关键词: Averaging principle;    Fast-slow system;    Mixed fractional Brownian rough path;    Fractional calculus approach;   

DOI  :  10.1016/j.jde.2021.08.006

来源: Elsevier

【 摘 要 】

This paper is devoted to studying the averaging principle for a fast-slow system of rough differential equations driven by mixed fractional Brownian rough path. The fast component is driven by Brownian motion, while the slow component is driven by fractional Brownian motion with Hurst index H (1/3 < H <= 1/2). Combining the fractional calculus approach to rough path theory and Khasminskii's classical time discretization method, we prove that the slow component strongly converges to the solution of the corresponding averaged equation in the L-1-sense. The averaging principle for a fast-slow system in the framework of rough path theory seems new. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free