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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 ISSN 0001-8708.
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Official URL: http://dx.doi.org/10.1016/j.aim.2016.02.011
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 | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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| Volume: | 293 | |||||||||
| Page Range: | pp. 720-737 | |||||||||
| DOI: | 10.1016/j.aim.2016.02.011 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | © 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 | |||||||||
| Date of first compliant deposit: | 22 July 2020 | |||||||||
| Date of first compliant Open Access: | 22 July 2020 | |||||||||
| RIOXX Funder/Project Grant: |
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