dc.date.accessioned | 2021-09-14T15:09:53Z | |
dc.date.available | 2021-09-14T15:09:53Z | |
dc.date.created | 2020-08-10T10:27:16Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Harang, Fabian Andsem Benth, Fred Espen . Infinite Dimensional Pathwise Volterra Processes Driven by Gaussian Noise -- Probabilistic Properties and Applications. Electronic Journal of Probability (EJP). 2021, 26 | |
dc.identifier.uri | http://hdl.handle.net/10852/88060 | |
dc.description.abstract | We investigate the probabilistic and analytic properties of Volterra processes constructed as pathwise integrals of deterministic kernels with respect to the Hölder continuous trajectories of Hilbert-valued Gaussian processes. To this end, we extend the Volterra sewing lemma from [18] to the two dimensional case, in order to construct two dimensional operator-valued Volterra integrals of Young type. We prove that the covariance operator associated to infinite dimensional Volterra processes can be represented by such a two dimensional integral, which extends the current notion of representation for such covariance operators. We then discuss a series of applications of these results, including the construction of a rough path associated to a Volterra process driven by Gaussian noise with possibly irregular covariance structures, as well as a description of the irregular covariance structure arising from Gaussian processes time-shifted along irregular trajectories. Furthermore, we consider an infinite dimensional fractional Ornstein-Uhlenbeck process driven by Gaussian noise, which can be seen as an extension of the volatility model proposed by Rosenbaum et al. | |
dc.language | EN | |
dc.rights | Attribution 4.0 International | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.title | Infinite Dimensional Pathwise Volterra Processes Driven by Gaussian Noise -- Probabilistic Properties and Applications | |
dc.type | Journal article | |
dc.creator.author | Harang, Fabian Andsem | |
dc.creator.author | Benth, Fred Espen | |
cristin.unitcode | 185,15,13,35 | |
cristin.unitname | Stokastisk, finans og risiko | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 1 | |
dc.identifier.cristin | 1822328 | |
dc.identifier.bibliographiccitation | info:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Electronic Journal of Probability (EJP)&rft.volume=26&rft.spage=&rft.date=2021 | |
dc.identifier.jtitle | Electronic Journal of Probability (EJP) | |
dc.identifier.volume | 26 | |
dc.identifier.startpage | 1 | |
dc.identifier.endpage | 42 | |
dc.identifier.doi | https://doi.org/10.1214/21-EJP683 | |
dc.identifier.urn | URN:NBN:no-90678 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 1083-6489 | |
dc.identifier.fulltext | Fulltext https://www.duo.uio.no/bitstream/handle/10852/88060/5/21-EJP683.pdf | |
dc.type.version | PublishedVersion | |
dc.relation.project | NFR/274410 | |