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arXiv · 1808.05903

A Non-vanishing Property for the Signature of a Path

Horatio Boedihardjo·Xi Geng
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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.

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Horatio Boedihardjo, Xi Geng. 2018-08-17. A Non-vanishing Property for the Signature of a Path. https://arxiv.org/abs/1808.05903

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