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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. [ABSTRACT FROM AUTHOR]

Stochastic differential equations (SDEs) on compact foliated spaces were introduced a few years ago. As a corollary, a leafwise Brownian motion on a compact foliated space was obtained as a solution to an SDE. In this paper we construct stochastic flows associated with the SDEs by using rough path theory, which is something like a "deterministic version" of Itô's SDE theory. [ABSTRACT FROM AUTHOR]