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A Levy-Cielsielski Expansion for Quantum Brownian Motion and the Construction of

Summary: A L´evy-Cielsielski Expansion for Quantum
Brownian Motion and the Construction of
Quantum Brownian Bridges
David Applebaum
Probability and Statistics Department,
University of Sheffield,
Hicks Building, Hounsfield Road,
Sheffield, England, S3 7RH
e-mail: D.Applebaum@sheffield.ac.uk
Dedicated to Robin Hudson on his 65th birthday.
We introduce "probabilistic" and "stochastic Hilbertian structures".
These seem to be a suitable context for developing a theory of "quan-
tum Gaussian processes". The Schauder system is utilised to give a
L´evy-Cielsielski representation of quantum Brownian motion as oper-
ators in Fock space over a space of square summable sequences. Quan-
tum Brownian bridges are defined and a number of representations of
these are given.
Keywords and phrases: daggered space, probabilistic Hilbertian
structure, stochastic Hilbertian structure, Fock space, exponential


Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield


Collections: Mathematics