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A Lévy-Ciesielski Expansion for Quantum Brownian Motion and the Construction of Quantum Brownian Bridges
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D. Applebaum
Published/Copyright:
June 9, 2010
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.
Key words and phrases.: 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
Received: 2007-02-08
Revised: 2007-05-31
Published Online: 2010-06-09
Published in Print: 2007-December
© Heldermann Verlag
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Articles in the same Issue
- Existence of Solutions for Unilateral Problems in L1 Involving Lower Order Terms in Divergence form in Orlicz Spaces
- On Strict Pseudoconvexity
- Differential Criterion of n-Dimensional Geometrically Convex Functions
- Continuity Properties of the Stress Tensor in the 3-Dimensional Ramberg/Osgood Model
- Weinstein's Technique for a Class of Parabolic Problems
- On the Uniqueness of Measure and Category σ-Ideals on 2ω
- -Best Approximation of a γ-Regular Function
- A Lévy-Ciesielski Expansion for Quantum Brownian Motion and the Construction of Quantum Brownian Bridges
- Generalized Vector Variational Inequalities in Topological Vector Spaces
- Erratum to the Paper “A Note on Stability of Solutions for Abstract Semilinear Dirichlet Problems”
