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Signature inversion for monotone paths

Abstract:
The aim of this article is to provide a simple sampling procedure to reconstruct any monotone path from its signature. For every N, we sample a lattice path of N steps with weights given by the coefficient of the corresponding word in the signature. We show that these weights on lattice paths satisfy the large deviations principle. In particular, this implies that the probability of picking up a “wrong” path is exponentially small in N. The argument relies on a probabilistic interpretation of the signature for monotone paths.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1214/17-ECP70

Authors


Duffield, N More by this author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Publisher:
University of Washington Publisher's website
Journal:
Electronic Communications in Probability Journal website
Volume:
22
Issue:
0
Pages:
1-11
Publication date:
2017-08-15
Acceptance date:
2017-06-23
DOI:
ISSN:
1083-589X
Pubs id:
pubs:725739
URN:
uri:3a25275b-ee2f-424d-9918-a4035986bc8b
UUID:
uuid:3a25275b-ee2f-424d-9918-a4035986bc8b
Local pid:
pubs:725739

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