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Non-commutative martingales and stochastic integrals in fock space

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Book cover Stochastic Processes in Quantum Theory and Statistical Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 173))

Abstract

Boson Pock space is used to construct some non-commutative martingales, and a definition of stochastic integrals based on exponential vectors is given. It is shown that Itô's formula reduces to the chain rule with Wick ordering.

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References

  1. Cockroft,A.M. and Hudson R.L., Quantum mechanical Wiener processes, J. Multivariate Anal. 7, 107–124 (1977).

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  2. Evans, D.E., Completely positive quasi-free maps on the CAR algebra, Commun. Math. Phys. 70, 53–68 (1979).

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  3. Guichardet, A., Symmetric Hilbert spaces and related topics, Springer lecture notes in mathematics 261, Springer,Berlin (1972).

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  4. Lipster, R.S. and Shirayev, A.N., Statistics of random processes I, General Theory, Springer, Berlin (1977).

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Author information

Authors and Affiliations

  1. Mathematics Department, University of Nottingham, University Park, NG7 2RD, Nottingham, England

    R. L. Hudson

  2. Mathematics Department, Bedford Cpllege, University of London, Regent's Park, NW1 4NS, London, England

    R. F. Streater

Authors
  1. R. L. Hudson
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  2. R. F. Streater
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Editor information

S. Albeverio Ph. Combe M. Sirugue-Collin

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© 1982 Springer-Verlag

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Hudson, R.L., Streater, R.F. (1982). Non-commutative martingales and stochastic integrals in fock space. In: Albeverio, S., Combe, P., Sirugue-Collin, M. (eds) Stochastic Processes in Quantum Theory and Statistical Physics. Lecture Notes in Physics, vol 173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11956-6_121

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  • DOI: https://doi.org/10.1007/3-540-11956-6_121

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11956-2

  • Online ISBN: 978-3-540-39546-1

  • eBook Packages: Springer Book Archive

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