Journal article

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

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APA Style

Chevyrev, I., & Lyons, T. (2016). Characteristic functions of measures on geometric rough paths. Annals of Probability, 44(6), 4049–4082.

MLA Style

Chevyrev, I., and T. Lyons. “Characteristic Functions of Measures on Geometric Rough Paths.” Annals of Probability, vol. 44, no. 6, Institute of Mathematical Statistics, 2016, pp. 4049–82.

Chicago Style

Chevyrev, I, and T Lyons. 2016. “Characteristic Functions of Measures on Geometric Rough Paths.” Annals of Probability 44 (6): 4049–82.
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Files:: AOP1068.pdf

(Preview, Version of record, pdf, 333.9KB, Terms of use)

Publisher copy:: 10.1214/15-AOP1068

Authors

+ Chevyrev, I More by this author

Institution:: University of Oxford
Oxford college:: St John's College
Role:: Author

+ Lyons, T More by this author

Institution:: University of Oxford
Oxford college:: St Anne's College
Role:: Author

+ European Research Council More from this funder

Grant:: 291244 Esig

Publisher:: Institute of Mathematical Statistics
Journal:: Annals of Probability More from this journal
Volume:: 44
Issue:: 6
Pages:: 4049-4082
Publication date:: 2016-11-14
Acceptance date:: 2015-10-12
DOI:: 10.1214/15-AOP1068
ISSN:: 0091-1798

Keywords:: 60B11 (Primary) 43A05 (Secondary)

math.PR
Pubs id:: pubs:502234
UUID:: uuid:93b42c41-14cd-431f-82b4-7eb662fd9d64
Local pid:: pubs:502234
Source identifiers:: 502234
Deposit date:: 2017-05-16

Terms of use

Copyright holder:: Institute of Mathematical Statistics
Copyright date:: 2016
Notes:: © Institute of Mathematical Statistics, 2016

Licence:: Terms and Conditions of Use for Oxford University Research Archive

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