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

• Autorzy: Applebaum D.
• Języki publikacji: EN

Abstrakty

EN

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 Levy-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.

Słowa kluczowe

EN

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

PL

układ Haara

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2007
• Tom: Vol. 13, nr 2
• Strony: 275--290
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Applebaum D.

• Probability and Statistics Department. University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, England,

Bibliografia

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