Delay equations driven by rough paths

  • In this article, we illustrate the flexibility of the algebraic integration formalism introduced in M. Gubinelli (2004), Controlling Rough Paths, J. Funct. Anal. 216, 86-140, 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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Metadaten
Author:Andreas Neuenkirch, Ivan Nourdin, Samy Tindel
URN:urn:nbn:de:hebis:30:3-328955
DOI:https://doi.org/10.1214/EJP.v13-575
ISSN:1083-6489
Parent Title (English):Electronic journal of probability
Publisher:EMIS ELibEMS
Place of publication:[Madralin]
Document Type:Article
Language:English
Year of Completion:2014
Date of first Publication:2008/11/11
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Release Date:2014/01/29
Tag:Malliavin calculus; delay equation; fractional Brownian motion; rough paths theory
Volume:13
Page Number:38
First Page:2031
Last Page:2068
Note:
This work is licensed under a Creative Commons Attribution 3.0 License http://creativecommons.org/licenses/by/3.0/ .
HeBIS-PPN:363711112
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G15 Gaussian processes
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H05 Stochastic integrals
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H07 Stochastic calculus of variations and the Malliavin calculus
Sammlungen:Universit├Ątspublikationen
Licence (German):License LogoCreative Commons - Namensnennung 3.0