Inverting the signature of a path

Terry Lyons; Weijun Xu

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arXiv · 1406.7833

Inverting the signature of a path

Terry Lyons·Weijun Xu

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Abstract

The aim of this article is to develop an explicit procedure that enables one to reconstruct any $C^1$ path (at natural parametrization) from its signature. We also explicitly quantify the distance between the reconstructed path and the original path in terms of the number of terms in the signature that are used for the construction and the modulus of continuity of the derivative of the path. A key ingredient in the construction is the use of a procedure of symmetrization that separates the behavior of the path at small and large scales.

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Terry Lyons, Weijun Xu. 2018-06-04. Inverting the signature of a path. https://arxiv.org/abs/1406.7833

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