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Flows Driven by Banach Space-Valued Rough Paths

  • Ismaël Bailleul
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2123)

Abstract

We show in this note how the machinery of \(\mathcal{C}^{1}\)-approximate flows devised in the work Flows driven by rough paths, and applied there to reprove and extend most of the results on Banach space-valued rough differential equations driven by a finite dimensional rough path can be used to deal with rough differential equations driven by an infinite dimensional Banach space-valued weak geometric Hölder p-rough paths, for any p > 2, giving back Lyons’ theory in its full force in a simple way.

Keywords

Flows Infinite dimensional rough paths Rough differential equations 

Notes

Acknowledgements

This research was partially supported by an ANR grant “Retour post-doctorant”. The author warmly thanks the UniversitÃl’ de Bretagne Occidentale where part of this work was written.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.IRMARRennesFrance

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