An Itô-Wentzell formula for rough paths

Abstract

This article shows an Itô-Wentzell type formula adapted to rough paths with $\alpha$-Hölder regularity $\alpha \in (\frac{1}{3},\frac{1}{2}]$. We improve previous results of R. Castrequini and P. Catuogno for the Young integral and C. Keller and J. Zhang for rough paths.