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Article Dans Une Revue Proceedings of the London Mathematical Society Année : 2020

The geometry of the space of branched Rough Paths

Résumé

We construct an explicit transitive free action of a Banach space of Hölder functions on the space of branched rough paths, which yields in particular a bijection between theses two spaces. This endows the space of branched rough paths the structure of a principal homogeneous space over a Banach space and allows to characterize its automorphisms. The construction is based on the Baker-Campbell-Hausdorff formula and on the Hairer-Kelly map, which allows to describe branched rough paths in terms of anisotropic geometric rough paths.
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Dates et versions

hal-01908559 , version 1 (30-10-2018)
hal-01908559 , version 2 (20-01-2020)

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Nikolas Tapia, Lorenzo Zambotti. The geometry of the space of branched Rough Paths. Proceedings of the London Mathematical Society, 2020, 121 (2), pp.220-251. ⟨10.1112/plms.12311⟩. ⟨hal-01908559v2⟩
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