Electronic Journal of Probability

Delay equations driven by rough paths

Andreas Neuenkirch, Ivan Nourdin, and Samy Tindel

Full-text: Open access

Abstract

In this article, we illustrate the flexibility of the algebraic integration formalism introduced in M. Gubinelli, <em>J. Funct. Anal.</em> <strong>216</strong>, 86-140, 2004, <a href="http://www.ams.org/mathscinet-getitem?mr=2005k:60169"> Math. Review 2005k:60169</a>, 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 <em>$H</em>>1/3$.

Article information

Source
Electron. J. Probab., Volume 13 (2008), paper no. 67, 2031-2068.

Dates
Accepted: 11 November 2008
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819140

Digital Object Identifier
doi:10.1214/EJP.v13-575

Mathematical Reviews number (MathSciNet)
MR2453555

Zentralblatt MATH identifier
1190.60046

Subjects
Primary: 60H05: Stochastic integrals
Secondary: 60H07: Stochastic calculus of variations and the Malliavin calculus 60G15: Gaussian processes

Keywords
rough paths theory delay equation fractional Brownian motion Malliavin calculus

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Neuenkirch, Andreas; Nourdin, Ivan; Tindel, Samy. Delay equations driven by rough paths. Electron. J. Probab. 13 (2008), paper no. 67, 2031--2068. doi:10.1214/EJP.v13-575. https://projecteuclid.org/euclid.ejp/1464819140


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References

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