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A non-vanishing property for the signature of a path

Boedihardjo, H. and Geng, X. (2019) A non-vanishing property for the signature of a path. Comptes Rendus Mathematique, 357 (2). pp. 120-129. ISSN 1631-073X

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To link to this item DOI: 10.1016/j.crma.2018.12.006

Abstract/Summary

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:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:81775
Publisher:Elsevier

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