Global Solutions to Rough Differential Equations with Unbounded Vector Fields

  • Antoine Lejay
Part of the Lecture Notes in Mathematics book series (LNM, volume 2046)


We give a sufficient condition to ensure the global existence of a solution to a rough differential equation whose vector field has a linear growth. This condition is weaker than the ones already given and may be used for geometric as well as non-geometric rough paths with values in any suitable (finite or infinite dimensional) space. For this, we study the properties the Euler scheme as done in the work of A.M. Davie.


Controlled differential equations Rough paths Euler scheme Global solution to differential equation Rough differential equation 


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This work has been supported by the ANR ECRU founded by the French Agence Nationale pour la Recherche. The author is also indebted to Massimiliano Gubinelli for interesting discussions about the topic. The author also wish to thank the anonymous referee for having suggested some improvements in the introduction.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Project-team TOSCAInstitut Elie Cartan Nancy (Nancy-Université, CNRS, INRIA)Vandœuvre-lès-NancyFrance

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