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Delay equations driven by rough paths

2008; Institute of Mathematical Statistics; Volume: 13; Issue: none Linguagem: Inglês

10.1214/ejp.v13-575

1083-6489

Andreas Neuenkirch, Ivan Nourdin, Samy Tindel,

Stochastic processes and statistical mechanics

In this article, we illustrate the flexibility of the algebraic integration formalism introduced in M. Gubinelli, J. Funct. Anal. 216 , 86-140, 2004, Math. Review 2005k:60169 , 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 $H >1/3$.