Pathwise integration with respect to paths of finite quadratic variation
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. T...
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| Format: | Journal article |
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Elsevier
2016
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| _version_ | 1826294076899590144 |
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| author | Ananova, A Cont, R |
| author_facet | Ananova, A Cont, R |
| author_sort | Ananova, A |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T03:40:03Z |
| format | Journal article |
| id | oxford-uuid:bd947570-ddc5-4d67-b96e-1df808a4af5a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:40:03Z |
| publishDate | 2016 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:bd947570-ddc5-4d67-b96e-1df808a4af5a2022-03-27T05:32:50ZPathwise integration with respect to paths of finite quadratic variationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bd947570-ddc5-4d67-b96e-1df808a4af5aSymplectic Elements at OxfordElsevier2016Ananova, ACont, RWe 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. |
| spellingShingle | Ananova, A Cont, R Pathwise integration with respect to paths of finite quadratic variation |
| title | Pathwise integration with respect to paths of finite quadratic variation |
| title_full | Pathwise integration with respect to paths of finite quadratic variation |
| title_fullStr | Pathwise integration with respect to paths of finite quadratic variation |
| title_full_unstemmed | Pathwise integration with respect to paths of finite quadratic variation |
| title_short | Pathwise integration with respect to paths of finite quadratic variation |
| title_sort | pathwise integration with respect to paths of finite quadratic variation |
| work_keys_str_mv | AT ananovaa pathwiseintegrationwithrespecttopathsoffinitequadraticvariation AT contr pathwiseintegrationwithrespecttopathsoffinitequadraticvariation |