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arXiv · 1508.06890

Reconstruction for the Signature of a Rough Path

Xi Geng
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Abstract

Recently it was proved that the group of rough paths modulo tree-like equivalence is isomorphic to the corresponding signature group through the signature map S (a generalized notion of taking iterated path integrals). However, the proof of this uniqueness result does not contain any information on how to "see" the trajectory of a (tree-reduced) rough path from its signature, and a constructive understanding on the uniqueness result (in particular on the inverse of S) has become an interesting and important question. The aim of the present paper is to reconstruct a rough path from its signature in an explicit and universal way.

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Xi Geng. 2016-11-09. Reconstruction for the Signature of a Rough Path. https://doi.org/10.1112/plms.12013

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