Markovian cocycles on operator algebras adapted to a Fock filtration

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dc.contributor.authorLindsay, J. Martinen
dc.contributor.authorWills, Stephen J.en
dc.date.accessioned2023-08-28T14:43:35Z
dc.date.available2023-08-28T14:43:35Z
dc.date.issued2000-12-20en
dc.description.abstractThe introduction of a Feller-type condition allows the study of Markovian, cocycles adapted to a Fock filtration to be extended from von Neumann algebras to C*-algebras. It is shown that every such cocycle which, along with its adjoint cocycle, is pointwise strongly continuous and whose associated semigroups are norm continuous, weakly satisfies a quantum stochastic differential equation (QSDE). The matrix of coefficients of this equation may thereby be considered as the generator of the cocycle. The QSDE is satisfied strongly in any of the following cases: when the cocycle is completely positive and contractive, or the driving quantum noise is finite dimensional, or the C*-algebra is finite dimensional and the cocycle generator is bounded. Applying the algebra results to Fock-adapted Markovian cocycles on a Hilbert space we obtain similar characterisations. In particular a contraction cocycle whose Markov semigroup is norm continuous strongly satisfies a QSDE. A representation of cocycles in terms of a family of associated semigroups is central to the present analysis, providing the connection with QSDEs through a parallel work (2000, J. M. Lindsay and S. J. Wills, Probab. Theory Related Fields 116, 505–543).en
dc.description.statusPeer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationLindsay, J.M. and Wills, S.J. (2000) ‘Markovian cocycles on operator algebras adapted to a Fock filtration’, Journal of Functional Analysis, 178(2), pp. 269–305. https://doi.org/10.1006/jfan.2000.3658.en
dc.identifier.doi10.1006/jfan.2000.3658en
dc.identifier.eissn1096-0783en
dc.identifier.endpage305en
dc.identifier.issn0022-1236en
dc.identifier.issued2en
dc.identifier.journaltitleJournal of Functional Analysisen
dc.identifier.startpage269en
dc.identifier.urihttps://hdl.handle.net/10468/14881
dc.identifier.volume178en
dc.language.isoenen
dc.publisherElsevieren
dc.relation.ispartofJournal of Functional Analysisen
dc.relation.urihttps://doi.org/10.1006/jfan.2000.3658en
dc.rights© 2000 by Academic Press. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0//en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0en
dc.subjectMarkovian cocycleen
dc.subjectStochastic flowen
dc.subjectQuantum stochasticen
dc.subjectCompletely boundeden
dc.subjectCompletely positiveen
dc.subjectQuantum Markov semigroupen
dc.subjectFeller propertyen
dc.titleMarkovian cocycles on operator algebras adapted to a Fock filtrationen
dc.typeArticle (peer-reviewed)en
oaire.citation.issue2en
oaire.citation.volume178en
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