Solving rough differential equations with the theory of regularity structures
Probability
2019-10-15 v4
Abstract
The purpose of this article is to solve rough differential equations with the theory of regularity structures. These new tools recently developed by Martin Hairer for solving semi-linear partial differential stochastic equations were inspired by the rough path theory. We take a pedagogical approach to facilitate the understanding of this new theory. We recover results of the rough path theory with the regularity structure framework. Hence, we show how to formulate a fixed point problem in the abstract space of modelled distributions to solve the rough differential equations. We also give a proof of the existence of a rough path lift with the theory of regularity structure.
Cite
@article{arxiv.1712.06285,
title = {Solving rough differential equations with the theory of regularity structures},
author = {Antoine Brault},
journal= {arXiv preprint arXiv:1712.06285},
year = {2019}
}