Delay equations driven by rough paths

TL;DR

This paper demonstrates the use of algebraic integration to establish existence and uniqueness for delay differential equations driven by rough paths, including fractional Brownian motion with Hurst parameter greater than 1/3.

Contribution

It introduces a novel application of algebraic integration to delay equations driven by rough signals, extending the theory to fractional Brownian motion.

Findings

Existence and uniqueness results for delay equations driven by rough paths.

Application to fractional Brownian motion with H>1/3.

Validation of algebraic integration in delay differential equations.

Abstract

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.