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A Lévy-Ciesielski expansion for quantum Brownian motion and the construction of quantum Brownian bridges

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

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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.

Item Type: Article
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.
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: 08 Feb 2013 16:59
Published Version: http://www.emis.de/journals/JAA/
Status: Published
Publisher: Heldermann Verlag
Refereed: Yes
URI: http://eprints.whiterose.ac.uk/id/eprint/9802

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