Flows driven by Banach space-valued rough paths

Ismaël Bailleul (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We show in this note how the machinery of C^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 Holder p-rough paths, for any p>2, giving back Lyons' theory in its full force in a simple way.

Mots clés: Flows; infinite dimensional rough paths; rough differential equations

Domaines: Probabilités [math.PR]; Analyse classique [math.CA]

Ismaël Bailleul. Flows driven by Banach space-valued rough paths. Donati-Martin Catherine, Lejay Antoine, Rouault Alain. Séminaire de Probabilités XLVI, 2123, Springer, pp.195-205, 2014, Lecture Notes in Mathematics, 978-3-319-11969-4. ⟨10.1007/978-3-319-11970-0_7⟩. ⟨hal-00905828⟩