A Non-vanishing Property for the Signature of a Path
Classical Analysis and ODEs
2018-12-24 v2
Abstract
We prove that a continuous path with finite length in a real Banach space cannot have infinitely many zero components in its signature unless it is tree-like. In particular, this allows us to strengthen a limit theorem for signature recently proved by Chang, Lyons and Ni. What lies at the heart of our proof is a complexification idea together with deep results from holomorphic polynomial approximations in the theory of several complex variables.
Keywords
Cite
@article{arxiv.1808.05903,
title = {A Non-vanishing Property for the Signature of a Path},
author = {Horatio Boedihardjo and Xi Geng},
journal= {arXiv preprint arXiv:1808.05903},
year = {2018}
}