Abstract
After reviewing theories of stochastic integration against Fock and non-Fock quantum Brownian motion, we prove a martingale representation theorem for the latter, extending the main result of [12] by incorporating an initial space. We construct unitary processes adapted to the filtration of non-Fock quantum Brownian motion and use the martingale representation theorem to characterise such processes in terms of covariantly adapted unitary evolutions [9] with a continuity property. The classical limits of the quantum dynamical semigroups associated with these processes are contrasted with those arising in the Fock case.
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Hudson, R.L., Lindsay, J.M. (1985). Uses of non-Fock quantum Brownian motion and a quantum martingale representation theorem. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications II. Lecture Notes in Mathematics, vol 1136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074480
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DOI: https://doi.org/10.1007/BFb0074480
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