Electronic Journal of Probability

On rough differential equations

Antoine Lejay

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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.

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

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

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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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