The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Journal of the European Mathematical Society

Full-Text PDF (247 KB) | Metadata | Table of Contents | JEMS summary
Online access to the full text of Journal of the European Mathematical Society is restricted to the subscribers of the journal, who are encouraged to communicate their IP-address(es) to their agent or directly to the publisher at
Volume 20, Issue 7, 2018, pp. 1655–1687
DOI: 10.4171/JEMS/796

Published online: 2018-05-22

Inverting the signature of a path

Terry J. Lyons[1] and Weijun Xu[2]

(1) University of Oxford, UK
(2) University of Warwick, Coventry, UK

The aim of this article is to develop an explicit procedure that enables one to reconstruct any $\mathcal C^1$ 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 behaviour of the path at small and large scales.

Keywords: Signature, inversion, symmetrization

Lyons Terry, Xu Weijun: Inverting the signature of a path. J. Eur. Math. Soc. 20 (2018), 1655-1687. doi: 10.4171/JEMS/796