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Inverting the signature of a path
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Lyons, Terry and Xu, Weijun (2018) Inverting the signature of a path. Journal of the European Mathematical Society, 20 (7). pp. 1655-1687. doi:10.4171/JEMS/796
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Official URL: https://doi.org/10.4171/JEMS/796
Abstract
The aim of this article is to develop an explicit procedure that enables one to reconstruct any C1 path (at natural parametrization) from its signature. We also explicitly quantify the distance between the reconstructed path and the original path in terms of the number of terms in the signature that are used for the construction and the modulus of continuity of the derivative of the path. A key ingredient in the construction is the use of a procedure of symmetrization that separates the behavior of the path at small and large scales.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Mathematics | ||||||
| Journal or Publication Title: | Journal of the European Mathematical Society | ||||||
| Publisher: | European Mathematical Society Publishing House | ||||||
| ISSN: | 1435-9855 | ||||||
| Official Date: | 22 May 2018 | ||||||
| Dates: |
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| Date of first compliant deposit: | 15 September 2016 | ||||||
| Volume: | 20 | ||||||
| Number: | 7 | ||||||
| Page Range: | pp. 1655-1687 | ||||||
| DOI: | 10.4171/JEMS/796 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
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