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

Abstract

This paper is devoted to studying the averaging principle for 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 $H(1/3<H\le 1/2)$. 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.

arXiv commentJournal of Differential Equations Volume 301, 15 November 2021, Pages 202-235

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Cited by in corpus (3)

• Slow-Fast Systems with Fractional Environment and Dynamics
• Generating diffusions with fractional Brownian motion
• Weak error estimates for rough volatility models