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Quantum stochastic integrals as belated integrals

Published online by Cambridge University Press:  18 May 2009

Chris Barnett ,
J. M. Lindsay  and
Ivan F. Wilde
Chris Barnett
Affiliation:
Department of Mathematics, Imperial College of Science, Technology and Medicine, London SW7 2BZ
J. M. Lindsay
Affiliation:
Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD
Ivan F. Wilde
Affiliation:
Department of Mathematics, Kings College, Strand, London WC2R 2LS
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Quantum stochastic integrals have been constructed in various contexts [2, 3, 4, 5, 9] by adapting the construction of the classical L2-Itô-integral with respect to Brownian motion. Thus, the integral is first defined for simple integrands as a finite sum, then one establishes certain isometry relations or suitable bounds to allow the extension, by continuity, to more general integrands. The integrator is typically operator-valued, the integrand is vector-valued or operator-valued and the quantum stochastic integral is then given as a vector in a Hilbert space, or as an operator on the Hilbert space determined by its action on suitable vectors.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 2 , May 1992 , pp. 165 - 173
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

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