Tohoku Mathematical Journal
2025
June
SECOND SERIES VOL. 77, NO. 2

Tohoku Math. J.
77 (2025), 189-227

Title AVERAGING PRINCIPLE FOR SLOW-FAST SYSTEMS OF ROUGH DIFFERENTIAL EQUATIONS VIA CONTROLLED PATHS

Author Yuzuru Inahama

(Received October 7, 2022, revised May 1, 2023)
Abstract. In this paper we prove the strong averaging principle for a slow-fast system of rough differential equations. The slow and the fast component of the system are driven by a rather general random rough path and Brownian rough path, respectively. These two driving noises are assumed to be independent. A prominent example of the driver of the slow component is fractional Brownian rough path with Hurst parameter between $1/3$ and $1/2$. We work in the framework of controlled path theory, which is one of the most widely-used frameworks in rough path theory. To prove our main theorem, we carry out Khas'minskiǐ's time-discretizing method in this framework.

Mathematics Subject Classification. Primary 60L90; Secondary 70K65, 70K70, 60F99.
Key words and phrases. Slow-fast system, averaging principle, rough path theory.

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