分野別セミナー

In this talk we discuss 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'minskii's
time-discretizing method in this framework.