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Pathwise integration with respect to paths of finite quadratic variation

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.
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https://hal.archives-ouvertes.fr/hal-01286515
Contributor : Rama Cont <>
Submitted on : Monday, August 29, 2016 - 6:12:58 PM
Last modification on : Saturday, March 28, 2020 - 2:08:07 AM
Document(s) archivé(s) le : Wednesday, November 30, 2016 - 2:32:50 PM

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  • HAL Id : hal-01286515, version 3

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Anna Ananova, Rama Cont. Pathwise integration with respect to paths of finite quadratic variation. 2016. ⟨hal-01286515v3⟩

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