Quasi-free stochastic integral representation theorems over the CCR

Quasi-free stochastic integral representation theorems over the CCR

It is shown that each vector in the Hilbert space of certain quasi-free representations of the CCR can be written uniquely in terms of quantum stochastic integrals. As a consequence, we obtain general vector-valued and operator-valued boson quantum martingale representation theorems.

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 1988-09, Vol.104 (2), p.383-398
1. Verfasser: Wilde, Ivan F.
Format: Artikel
Sprache:eng
Schlagworte:
Exact sciences and technology
Mathematical methods in physics
Physics
Probability theory, stochastic processes, and statistics
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Zusammenfassung:It is shown that each vector in the Hilbert space of certain quasi-free representations of the CCR can be written uniquely in terms of quantum stochastic integrals. As a consequence, we obtain general vector-valued and operator-valued boson quantum martingale representation theorems.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004100065543