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Flows Driven by Banach Space-Valued Rough Paths

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Séminaire de Probabilités XLVI

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,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.

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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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Authors and Affiliations

  1. IRMAR, 263 Av. du General Leclerc, 35042, Rennes, France

    Ismaël Bailleul

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  1. Ismaël Bailleul
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Correspondence to Ismaël Bailleul .

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Editors and Affiliations

  1. Université de Versailles-St-Quentin Laboratoire de Mathématiques, Versailles, France

    Catherine Donati-Martin

  2. INRIA, Nancy-Université, Vandoeuvre-lès-Nancy, France

    Antoine Lejay

  3. Laboratoire de Mathématiques, Université de Versailles-St-Quentin, Versailles, France

    Alain Rouault

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Bailleul, I. (2014). Flows Driven by Banach Space-Valued Rough Paths. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLVI. Lecture Notes in Mathematics(), vol 2123. Springer, Cham. https://doi.org/10.1007/978-3-319-11970-0_7

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