Abstract
We discuss the relation between the mutual quadratic variation of two measures and the Ito table in quantum stochastic calculus. We prove the existence of the mutual quadratic variation of field- and gauge-measures in a quasi-free representation of the CCR in the topology of strong convergence on an appropriate invariant domain. We characterise the Fock state in terms of the mutual quadratic variation of the field-and gauge-measures. The higher order quadratic variations of these measures are computed in a general quasi-free representation.
Keywords
- Strong Convergence
- Quadratic Variation
- Topological Algebra
- Gauge Measure
- Strong Operator Topology
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References
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R.L. Hudson, J.M. Lindsay; Stochastic integration and a martingale representation theorem for non-Fock quantum Brownian motion, J. Funct. Anal. 61, 202–221 (1985)
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© 1988 Springer-Verlag
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Quaegebeur, J. (1988). Mutual quadratic variation and ito's table in quantum stochastic calculus. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications III. Lecture Notes in Mathematics, vol 1303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078068
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DOI: https://doi.org/10.1007/BFb0078068
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18919-0
Online ISBN: 978-3-540-38846-3
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