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

Bin Pei, Yuzuru Inahama, Yong Xu

Research output: Contribution to journalArticlepeer-review

Abstract

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 L1-sense. The averaging principle for a fast-slow system in the framework of rough path theory seems new.

Original languageEnglish
Pages (from-to)202-235
Number of pages34
JournalJournal of Differential Equations
Volume301
DOIs
Publication statusPublished - Nov 15 2021

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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