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A Lévy-Ciesielski Expansion for Quantum Brownian Motion and the Construction of Quantum Brownian Bridges

A Lévy-Ciesielski Expansion for Quantum Brownian Motion and the Construction of Quantum Brownian... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Analysis de Gruyter

A Lévy-Ciesielski Expansion for Quantum Brownian Motion and the Construction of Quantum Brownian Bridges

Journal of Applied Analysis , Volume 13 (2) – Dec 1, 2007

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References (29)

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1425-6908
eISSN
1869-6082
DOI
10.1515/JAA.2007.275
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Journal of Applied Analysisde Gruyter

Published: Dec 1, 2007

Keywords: Daggered space; probabilistic Hilbertian structure; stochastic Hilbertian structure; Fock space; exponential vector; quantum Brownian motion; Haar system; Schauder system; Lévy-Ciesielski expansion; quantum Brownian bridge

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