Solving rough differential equations with the theory of regularity structures

Antoine Brault

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arXiv · 1712.06285

Solving rough differential equations with the theory of regularity structures

Antoine Brault

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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.

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BibTeX RIS

Antoine Brault. 2017-12-18. Solving rough differential equations with the theory of regularity structures. https://arxiv.org/abs/1712.06285

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