Electronic Journal of Probability

On rough differential equations

Antoine Lejay

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Abstract

We prove that the Itô map, that is the map that gives the solution of a differential equation controlled by a rough path of finite $p$-variation with $p\in [2,3)$ is locally Lipschitz continuous in all its arguments and we give some sufficient conditions for global existence for non-bounded vector fields.

Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 12, 341-364.

Dates
Accepted: 2 February 2009
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819473

Digital Object Identifier
doi:10.1214/EJP.v14-613

Mathematical Reviews number (MathSciNet)
MR2480544

Zentralblatt MATH identifier
1190.60044

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

Citation

Lejay, Antoine. On rough differential equations. Electron. J. Probab. 14 (2009), paper no. 12, 341--364. doi:10.1214/EJP.v14-613. https://projecteuclid.org/euclid.ejp/1464819473


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