Reflected rough differential equations via controlled paths

TL;DR

This paper advances the theory of reflected rough differential equations by establishing an existence theorem under weaker assumptions, utilizing Gubinelli's controlled path framework to improve upon previous Euler approximation methods.

Contribution

It introduces a new existence proof for reflected rough differential equations using controlled paths, relaxing earlier assumptions and extending the theoretical foundation.

Findings

Existence of solutions under weaker conditions

Application of Gubinelli's controlled paths to reflected equations

Improved theoretical understanding of rough differential equations

Abstract

In [1], we proved the existence of solutions to reflected rough differential equations based on an idea of Euler approximation of the solutions which is due to Davie [6]. In this paper, we prove the existence theorem under weaker assumptions than those in [1] by using the notion of Gubinelli's controlled path [14].