Delay equations driven by rough paths. (English) Zbl 1190.60046

Neuenkirch, Andreas; Nourdin, Ivan; Tindel, Samy

Electron. J. Probab. 13, 2031-2068 (2008).

Summary: We illustrate the flexibility of the algebraic integration formalism introduced in [M. Gubinelli, J. Funct. Anal. 216, No. 1, 86–140 (2004; Zbl 1058.60037)], 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 \(H>1/3\).

MSC:

60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60H05	Stochastic integrals
60H07	Stochastic calculus of variations and the Malliavin calculus
60G15	Gaussian processes

Keywords:

rough paths theory; delay equation; fractional Brownian motion; Malliavin calculus

Citations:

Zbl 1058.60037