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 doi: 10.1016/j.aim.2016.02.011

Abstract/Summary

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
URI	https://reading-clone.eprints-hosting.org/id/eprint/58182
Identification Number/DOI	10.1016/j.aim.2016.02.011
Refereed	No
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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