The geometry of the space of branched rough paths

Autor: Lorenzo Zambotti, Nikolas Tapia
Přispěvatelé: Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin] (WIAS), Forschungsverbund Berlin e.V. (FVB) (FVB), Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut für Mathematik [Berlin], Technische Universität Berlin (TU), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Forschungsverbund Berlin e.V. (FVB), Technische Universität Berlin (TUB), Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001))
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Proceedings of the London Mathematical Society
Proceedings of the London Mathematical Society, London Mathematical Society, 2020, 121 (2), pp.220-251. ⟨10.1112/plms.12311⟩
ISSN: 0024-6115
DOI: 10.1112/plms.12311⟩
Popis: We construct an explicit transitive free action of a Banach space of H\"older 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.
Comment: Final version to appear in Proceedings of the London Mathematical Society. 34 pages
Databáze: OpenAIRE
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