Flows driven by banach space-valued rough paths

Abstract

We show in this note how the machinery of E 1-approximate flows devised in the work Flows driven by rough paths, and applied there to reprove and extend most of the results on Banach space-valued rough differential equations driven by a finite dimensional rough path can be used to deal with rough differential equations driven by an infinite dimensional Banach space-valued weak geometric Hölder p-rough paths, for any p > 2, giving back Lyons’ theory in its full force in a simple way.