Delay equations driven by rough paths

2007/11/16 by Andreas Neuenkirch, Neuenkirch, Andreas, Ivan Nourdin +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60G15 #60H05 #60H07 #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.0711.2633

openalex publication_date 2007/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Unbiased Rough Integrators and No Free Lunch in Rough-Path-Based Market Models

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