The geometry of the space of branched Rough Paths
Probability
2020-03-20 v5
Abstract
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.
Keywords
Cite
@article{arxiv.1810.12179,
title = {The geometry of the space of branched Rough Paths},
author = {Nikolas Tapia and Lorenzo Zambotti},
journal= {arXiv preprint arXiv:1810.12179},
year = {2020}
}
Comments
Final version to appear in Proceedings of the London Mathematical Society. 34 pages