Applebaum, D. (2007) A Lévy-Ciesielski expansion for quantum Brownian motion and the construction of quantum Brownian bridges. Journal of Applied Analysis, 13 (2). pp. 275-290. ISSN 1425-6908
Abstract
We introduce "probabilistic" and "stochastic Hilbertian structures". These seem to be a suitable context for developing a theory of "quantum Gaussian processes". The Schauder system is utilised to give a Lévy-Ciesielski representation of quantum (bosonic) Brownian motion as operators in Fock space over a space of square summable sequences. Similar results hold for non-Fock, fermion, free and monotone Brownian motions. Quantum Brownian bridges are defined and a number of representations of these are given.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2007 Heldermann Verlag. This is an author produced version of a paper subsequently published in Journal of Applied Analysis. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Daggered space, probabilistic Hilbertian structure, stochastic Hilbertian structure, Fock space, exponential vector, quantum Brownian motion, Haar system, Schauder system, Levy-Ciesielski expansion, quantum Brownian bridge. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Miss Anthea Tucker |
Date Deposited: | 30 Sep 2009 11:42 |
Last Modified: | 16 Nov 2015 11:48 |
Published Version: | http://www.emis.de/journals/JAA/ |
Status: | Published |
Publisher: | Heldermann Verlag |
Refereed: | Yes |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:9802 |