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A non-vanishing property for the signature of a path
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Boedihardjo, Horatio and Geng, Xi (2019) A non-vanishing property for the signature of a path. Comptes Rendus Mathematique, 357 (2). pp. 120-129. doi:10.1016/j.crma.2018.12.006
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Official URL: https://doi.org/10.1016/j.crma.2018.12.006
Abstract
We prove that a continuous path with finite length in a real Banach space cannot have infinitely many zero components in its signature unless it is tree-like. In particular, this allows us to strengthen a limit theorem for signature recently proved by Chang, Lyons and Ni. What lies at the heart of our proof is a complexification idea together with deep results from holomorphic polynomial approximations in the theory of several complex variables.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Statistics | ||||||
| Journal or Publication Title: | Comptes Rendus Mathematique | ||||||
| Publisher: | Elsevier | ||||||
| ISSN: | 1631-073X | ||||||
| Official Date: | February 2019 | ||||||
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| Volume: | 357 | ||||||
| Number: | 2 | ||||||
| Page Range: | pp. 120-129 | ||||||
| DOI: | 10.1016/j.crma.2018.12.006 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
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