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.
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}
}