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Pathwise integration with respect to paths of finite quadratic variation

Subtitle:
Intégration trajectorielle par rapport à des trajectoires de variation quadratique finie
Abstract:

We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property, analogous to the well-known Ito isometry for stochastic integrals. This property is then used to represent the integral as a continuous map on an appropriately defined vector space of integrands. Finally, we obtain a pathwise ‘signal plus noise’ decomposition for r...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's Version

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Publisher copy:
10.1016/j.matpur.2016.10.004

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Hughs College
Role:
Author
ORCID:
0000-0003-1164-6053
Publisher:
Elsevier Publisher's website
Journal:
Journal de Mathématiques Pures et Appliquées Journal website
Volume:
107
Issue:
6
Pages:
737-757
Publication date:
2016-10-29
Acceptance date:
2016-08-10
DOI:
EISSN:
0021-7824
ISSN:
1776-3371
Pubs id:
pubs:866699
URN:
uri:bd947570-ddc5-4d67-b96e-1df808a4af5a
UUID:
uuid:bd947570-ddc5-4d67-b96e-1df808a4af5a
Local pid:
pubs:866699

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