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The signature of a rough path : uniqueness

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Boedihardjo, Horatio, Geng, Xi, Lyons, Terry and Yang, Danyu (2016) The signature of a rough path : uniqueness. Advances in Mathematics, 293 . pp. 720-737. doi:10.1016/j.aim.2016.02.011

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Official URL: http://dx.doi.org/10.1016/j.aim.2016.02.011

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Abstract

In the context of controlled differential equations, the signature is the exponential function on paths. B. Hambly and T. Lyons proved that the signature of a bounded variation path is trivial if and only if the path is tree-like. We extend Hambly–Lyons' result and their notion of tree-like paths to the setting of weakly geometric rough paths in a Banach space. At the heart of our approach is a new definition for reduced path and a lemma identifying the reduced path group with the space of signatures.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Stochastic differential equations, Differential equations, Exponential functions, Banach spaces
Journal or Publication Title: Advances in Mathematics
Publisher: Academic Press
ISSN: 0001-8708
Official Date: 30 April 2016
Dates:
DateEvent
30 April 2016Published
6 February 2016Accepted
Date of first compliant deposit: 22 July 2020
Volume: 293
Page Range: pp. 720-737
DOI: 10.1016/j.aim.2016.02.011
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: © 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/.
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
291244European Research Councilhttp://dx.doi.org/10.13039/501100000781
EP/F029578/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266

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