Delay equations driven by rough paths

Andreas Neuenkirch (1) , Ivan Nourdin (2) , Samy Tindel (3)

1 Institut für Mathematik
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 IECN - Institut Élie Cartan de Nancy

In this article, we illustrate the flexibility of the algebraic integration formalism introduced by M. Gubinelli (2004), by establishing an existence and uniqueness result for delay equations driven by rough paths. We then apply our results to the case where the driving path is a fractional Brownian motion with Hurst parameter H>1/3.

Mots clés: rough paths theory; delay equation; fractional Brownian motion; Malliavin calculus

Domaines: Probabilités [math.PR]

Andreas Neuenkirch, Ivan Nourdin, Samy Tindel. Delay equations driven by rough paths. Electronic Journal of Probability, 2008, 45, pp.2031-2068. ⟨hal-00188368⟩