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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.
Journal of Applied Analysis – de 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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