Ni, H;
Lyons, T;
Chang, J;
(2018)
Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length.
Comptes Rendus Mathématique
, 365
(7)
pp. 720-724.
10.1016/j.crma.2018.05.010.
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Abstract
For a path of length L>0, if for all n≥1, we multiply the n-th term of the signature by n!L−n, we say that the resulting signature is ‘normalised’. It has been established (T. J. Lyons, M. Caruana, T. Lévy, Differential equations driven by rough paths, Springer, 2007) that the norm of the n-th term of the normalised signature of a bounded-variation path is bounded above by 1. In this article, we discuss the super-multiplicativity of the norm of the signature of a path with finite length, and prove by Fekete's lemma the existence of a non-zero limit of the n-th root of the norm of the n-th term in the normalised signature as n approaches infinity.
| Type: | Article |
|---|---|
| Title: | Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.crma.2018.05.010 |
| Publisher version: | https://doi.org/10.1016/j.crma.2018.05.010 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10049771 |
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