Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 301, Issue -, Pages 202-235Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2021.08.006
Keywords
Averaging principle; Fast-slow system; Mixed fractional Brownian rough path; Fractional calculus approach
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Funding
- JSPS for Postdoctoral Fellowships for Research in Japan
- National Natural Science Foundation of China [12072264, 11802216]
- Fundamental Research Funds for the Central Universities
- Young Talent fund of University Association for Science and Technology in Shaanxi, China
- JSPS [JP18F18314]
- JSPS KAKENHI [JP20H01807]
- Shaanxi Provincial Key RD Program [2019TD-010, 2020KW-013]
- Northwestern Polytechnical University
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This paper investigates the averaging principle for a fast-slow system of rough differential equations driven by mixed fractional Brownian rough path, where the slow component strongly converges to the solution of the corresponding averaged equation in the L-1-sense. The proposed averaging principle for a fast-slow system in the framework of rough path theory appears to be novel.
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.
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