English

Multiscale systems, homogenization, and rough paths

Dynamical Systems 2019-06-18 v2 Probability

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 pp-variation and c\`adl\`ag rough path theory.

Keywords

Cite

@article{arxiv.1712.01343,
  title  = {Multiscale systems, homogenization, and rough paths},
  author = {Ilya Chevyrev and Peter K. Friz and Alexey Korepanov and Ian Melbourne and Huilin Zhang},
  journal= {arXiv preprint arXiv:1712.01343},
  year   = {2019}
}

Comments

27 pages. Minor corrections. To appear in Proceedings of the Conference in Honor of the 75th Birthday of S.R.S. Varadhan

R2 v1 2026-06-22T23:06:31.402Z