Inverting the signature of a path

Author: 

Lyons, T
Xu, W

Publication Date: 

22 May 2018

Journal: 

Journal of the European Mathematical Society

Last Updated: 

2021-03-21T08:05:29.027+00:00

Issue: 

7

Volume: 

20

DOI: 

10.4171/JEMS/796

page: 

1655-1687

abstract: 

The aim of this article is to develop an explicit procedure that enables one
to reconstruct any $C^1$ 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.

Symplectic id: 

502231

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article