# Multiscale systems, homogenization, and rough paths

Chevyrev, I
Friz, P
Korepanov, A
Melbourne, I
Zhang, H

## Journal:

VAR75 2016: Probability and Analysis in Interacting Physical Systems. Springer (2019) pp 17-48

## Last Updated:

2019-07-03T08:47:36.513+01:00

## DOI:

10.1007/978-3-030-15338-0_2

## abstract:

In recent years, substantial progress was made towards understanding
convergence of fast-slow deterministic systems to stochastic differential
equations. In contrast to more classical approaches, the assumptions on the
fast flow are very mild. We survey the origins of this theory and then revisit
and improve the analysis of Kelly-Melbourne [Ann. Probab. Volume 44, Number 1
(2016), 479-520], taking into account recent progress in $p$-variation and
c\adl\ag rough path theory.

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