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The signature of a rough path: uniqueness

Boedihardjo, H., Geng, X., Lyons, T. and Yang, D. (2016) The signature of a rough path: uniqueness. Advances in Mathematics, 293. pp. 720-737. ISSN 1090-2082

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To link to this item DOI: 10.1016/j.aim.2016.02.011


In the context of controlled differential equations, the signature is the exponential function on paths. B. Hambly and T. Lyons proved that the signature of a bounded variation path is trivial if and only if the path is tree-like. We extend Hambly–Lyons' result and their notion of tree-like paths to the setting of weakly geometric rough paths in a Banach space. At the heart of our approach is a new definition for reduced path and a lemma identifying the reduced path group with the space of signatures.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:58182


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