The geometry of the space of branched Rough Paths
arXiv:1810.12179 · doi:10.1112/plms.12311
Abstract
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 with 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, on a constructive version of the Lyons-Victoir extension theorem and on the Hairer-Kelly map, which allows to describe branched rough paths in terms of anisotropic geometric rough paths.
arXiv commentFinal version to appear in Proceedings of the London Mathematical Society. 34 pages
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