dc.contributor.author | Benth, Fred Espen | |
dc.contributor.author | Galimberti, Luca | |
dc.date.accessioned | 2022-12-29T13:22:29Z | |
dc.date.available | 2022-12-29T13:22:29Z | |
dc.date.created | 2022-05-16T15:46:15Z | |
dc.date.issued | 2022 | |
dc.identifier.citation | Infinite Dimensional Analysis Quantum Probability and Related Topics. 2022, 25 (2), 1-35. | en_US |
dc.identifier.issn | 0219-0257 | |
dc.identifier.uri | https://hdl.handle.net/11250/3039904 | |
dc.description.abstract | We provide a detailed analysis of the Gelfand integral on Fréchet spaces, showing among other things a Vitali theorem, dominated convergence and a Fubini result. Furthermore, the Gelfand integral commutes with linear operators. The Skorohod integral is conveniently expressed in terms of a Gelfand integral on Hida distribution space, which forms our prime motivation and example. We extend several results of Skorohod integrals to a general class of pathwise Gelfand integrals. For example, we provide generalizations of the Hida–Malliavin derivative and extend the integration-by-parts formula in Malliavin Calculus. A Fubini-result is also shown, based on the commutative property of Gelfand integrals with linear operators. Finally, our studies give the motivation for two existing definitions of stochastic Volterra integration in Hida space. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | World Scientific Publishing | en_US |
dc.title | Stochastic integrals and Gelfand integration in Fréchet spaces | en_US |
dc.title.alternative | Stochastic integrals and Gelfand integration in Fréchet spaces | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | acceptedVersion | en_US |
dc.rights.holder | This article will not be available until March 30, 2023 due to publisher embargo | en_US |
dc.source.pagenumber | 1-35 | en_US |
dc.source.volume | 25 | en_US |
dc.source.journal | Infinite Dimensional Analysis Quantum Probability and Related Topics | en_US |
dc.source.issue | 2 | en_US |
dc.identifier.doi | 10.1142/S0219025722500072 | |
dc.identifier.cristin | 2024950 | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |