Delay equations driven by rough paths

Abstract

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 $H>1/3$.

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