Journal article

Reconstruction for the signature of a rough path

Xi Geng

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | WILEY | Published : 2017

Abstract

Recently, it was proved that the group of rough paths modulo tree-like equivalence is isomorphic to the corresponding signature group through the signature map S (a generalized notion of taking iterated path integrals). However, the proof of this uniqueness result does not contain any information on how to 'see' the trajectory of a (tree-reduced) rough path from its signature, and a constructive understanding on the uniqueness result (in particular, on the inverse of S) has become an interesting and important question. The aim of this paper is to reconstruct a rough path from its signature in an explicit and universal way.

University of Melbourne Researchers

Grants

Awarded by ERC grant


Funding Acknowledgements

The author is supported by the ERC grant (grant agreement no. 291244 Esig).