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The signature of a rough path: Uniqueness

Abstract:
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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.aim.2016.02.011

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Institution:
University of Oxford
Oxford college:
St Anne's College
Role:
Author
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Institution:
University of Oxford
Oxford college:
Balliol College
Role:
Author
291244 Esig/ERC More from this funder
EP/F029578/1/EPSRC More from this funder
Publisher:
Elsevier Publisher's website
Journal:
Advances in Mathematics Journal website
Volume:
293
Pages:
720-737
Publication date:
2016-03-04
Acceptance date:
2016-02-08
DOI:
EISSN:
1090-2082
ISSN:
0001-8708
Source identifiers:
502237
Keywords:
Pubs id:
pubs:502237
UUID:
uuid:820ab9d3-7043-45c7-ab2b-aab57680f0d9
Local pid:
pubs:502237
Deposit date:
2017-08-24

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