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.
Keywords :
Type de document :
Pré-publication, Document de travail
A paraitre dans: Journal de Mathématiques Pures et Appliquées. 2016
Domaine :

https://hal.archives-ouvertes.fr/hal-01286515
Contributeur : Rama Cont <>
Soumis le : lundi 29 août 2016 - 18:12:58
Dernière modification le : lundi 29 mai 2017 - 14:27:19
Document(s) archivé(s) le : mercredi 30 novembre 2016 - 14:32:50

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PathwiseIsometry.pdf
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• HAL Id : hal-01286515, version 3

Citation

Anna Ananova, Rama Cont. Pathwise integration with respect to paths of finite quadratic variation. A paraitre dans: Journal de Mathématiques Pures et Appliquées. 2016. <hal-01286515v3>

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