Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length

Author: 

Chang, J
Lyons, T
Ni, H

Publication Date: 

1 July 2018

Journal: 

Comptes Rendus Mathematique

Last Updated: 

2019-04-26T22:23:55.193+01:00

Issue: 

7

Volume: 

356

DOI: 

10.1016/j.crma.2018.05.010

page: 

720-724

abstract: 

© 2018 Académie des sciences 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.

Symplectic id: 

852210

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article