English

Insertion algorithm for inverting the signature of a path

Probability 2019-07-22 v1 Numerical Analysis Numerical Analysis

Abstract

In this article we introduce the insertion method for reconstructing the path from its signature, i.e. inverting the signature of a path. For this purpose, we prove that a converging upper bound exists for the difference between the inserted n-th term and the (n+1)-th term of the normalised signature of a smooth path, and we also show that there exists a constant lower bound for a subsequence of the terms in the normalised signature of a piecewise linear path. We demonstrate our results with numerical examples.

Keywords

Cite

@article{arxiv.1907.08423,
  title  = {Insertion algorithm for inverting the signature of a path},
  author = {Jiawei Chang and Terry Lyons},
  journal= {arXiv preprint arXiv:1907.08423},
  year   = {2019}
}
R2 v1 2026-06-23T10:25:05.751Z