Rough path theory and an introduction to rough partial differential equations

TL;DR

This paper introduces rough path theory and its application to rough partial differential equations, providing foundational concepts and discussing stochastic PDE applications.

Contribution

It offers an accessible introduction to rough PDEs and integrates rough path theory with stochastic PDE applications.

Findings

Provides foundational understanding of rough PDEs

Connects rough path theory with stochastic PDEs

Serves as an introductory resource for the field

Abstract

The goal of these notes is to provide an introduction to rough partial differential equations. For this purpose, we will present the theory of rough paths to the extend as it is required. Applications to stochastic partial differential equations are presented as well.