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

    20 Citations (Scopus)

    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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