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Pathwise integration with respect to paths of finite quadratic variation

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Title: Pathwise integration with respect to paths of finite quadratic variation
Authors: Cont, R
Ananova, A
Item Type: Journal Article
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 regular functionals of an irregular path with non-vanishing quadratic variation, as a unique sum of a pathwise integral and a component with zero quadratic variation.
Issue Date: 29-Oct-2016
Date of Acceptance: 10-Aug-2016
URI: http://hdl.handle.net/10044/1/39595
DOI: https://dx.doi.org/10.1016/j.matpur.2016.10.004
ISSN: 0021-7824
Publisher: Elsevier
Start Page: 737
End Page: 757
Journal / Book Title: Journal de Mathematiques Pures et Appliquees
Volume: 107
Issue: 6
Copyright Statement: © 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords: math.PR
60H05 26B15
pathwise stochastic integration
Ito isometry
stochastic integral
Riemann sum
quadratic variation
0101 Pure Mathematics
0102 Applied Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Financial Mathematics
Faculty of Natural Sciences