dc.date.accessioned | 2021-04-30T19:41:46Z | |
dc.date.available | 2021-08-16T22:45:47Z | |
dc.date.created | 2021-03-24T10:45:17Z | |
dc.date.issued | 2020 | |
dc.identifier.citation | Benth, Fred Espen Detering, Nils Krühner, Paul . Independent increment processes: a multilinearity preserving property. Stochastics: An International Journal of Probability and Stochastic Processes. 2020 | |
dc.identifier.uri | http://hdl.handle.net/10852/85799 | |
dc.description.abstract | We observe a multilinearity preserving property of conditional expectation for infinite-dimensional independent increment processes defined on some abstract Banach space B. It is similar in nature to the polynomial preserving property analysed greatly for finite-dimensional stochastic processes and thus offers an infinite-dimensional generalization. However, while polynomials are defined using the multiplication operator and as such require a Banach algebra structure, the multilinearity preserving property we prove here holds even for processes defined on a Banach space which is not necessarily a Banach algebra. In the special case of B being a commutative Banach algebra, we show that independent increment processes are polynomial processes in a sense that coincides with a canonical extension of polynomial processes from the finite-dimensional case. The assumption of commutativity is shown to be crucial and in a non-commutative Banach algebra the multilinearity concept arises naturally. Some of our results hold beyond independent increment processes and thus shed light on infinite-dimensional polynomial processes in general. | |
dc.language | EN | |
dc.title | Independent increment processes: a multilinearity preserving property | |
dc.type | Journal article | |
dc.creator.author | Benth, Fred Espen | |
dc.creator.author | Detering, Nils | |
dc.creator.author | Krühner, Paul | |
cristin.unitcode | 185,15,13,0 | |
cristin.unitname | Matematisk institutt | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 1 | |
dc.identifier.cristin | 1900546 | |
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=Stochastics: An International Journal of Probability and Stochastic Processes&rft.volume=&rft.spage=&rft.date=2020 | |
dc.identifier.jtitle | Stochastics: An International Journal of Probability and Stochastic Processes | |
dc.identifier.startpage | 1 | |
dc.identifier.endpage | 30 | |
dc.identifier.doi | https://doi.org/10.1080/17442508.2020.1802458 | |
dc.identifier.urn | URN:NBN:no-88486 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 1744-2508 | |
dc.identifier.fulltext | Fulltext https://www.duo.uio.no/bitstream/handle/10852/85799/1/IndependentIncrementMultilinearRevision.pdf | |
dc.type.version | AcceptedVersion | |