Inverting the signature of a path

  • Terry J. Lyons

    University of Oxford, UK
  • Weijun Xu

    University of Warwick, Coventry, UK


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

Cite this article

Terry J. Lyons, Weijun Xu, Inverting the signature of a path. J. Eur. Math. Soc. 20 (2018), no. 7, pp. 1655–1687

DOI 10.4171/JEMS/796