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Main Title: The geometry of the space of branched rough paths
Author(s): Tapia, Nikolas
Zambotti, Lorenzo
Type: Article
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 these 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.
Subject(s): 60H10 (primary)
16T05 (secondary)
Issue Date: 18-Mar-2020
Date Available: 16-Dec-2020
Language Code: en
DDC Class: 510 Mathematik
Journal Title: Proceedings of the London Mathematical Society
Publisher: Wiley
Volume: 121
Issue: 2
Publisher DOI: 10.1112/plms.12311
Page Start: 220
Page End: 251
EISSN: 1460-244X
ISSN: 0024-6115
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik » AG Stochastik und Finanzmathematik
Appears in Collections:Technische Universität Berlin » Publications

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