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Characteristic functions of measures on geometric rough paths

Abstract:
We define a characteristic function for probability measures on the signatures of geometric rough paths. We determine sufficient conditions under which a random variable is uniquely determined by its expected signature, thus partially solving the analogue of the moment problem. We furthermore study analyticity properties of the characteristic function and prove a method of moments for weak convergence of random variables. We apply our results to signature arising from Lévy, Gaussian and Markovian rough paths.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1214/15-AOP1068

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Institution:
University of Oxford
Department:
St Johns College
More by this author
Institution:
University of Oxford
Department:
St Annes College
Publisher:
Institute of Mathematical Statistics Publisher's website
Journal:
Annals of Probability Journal website
Volume:
44
Issue:
6
Pages:
4049-4082
Publication date:
2016-11-14
Acceptance date:
2015-10-12
DOI:
ISSN:
0091-1798
Pubs id:
pubs:502234
URN:
uri:93b42c41-14cd-431f-82b4-7eb662fd9d64
UUID:
uuid:93b42c41-14cd-431f-82b4-7eb662fd9d64
Local pid:
pubs:502234

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