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Quantum stochastic integration and quantum stochastic differential equations

Published online by Cambridge University Press:  24 October 2008

Chris Barnett ,
Stanisław Goldstein  and
Ivan Wilde
Chris Barnett
Affiliation:
Department of Mathematics, Imperial College of Science, Technology and Medicine, London SW7 2BZ
Stanisław Goldstein
Affiliation:
Institute of Mathematics, Łódź University, ul. Banacha 22, 90-238 Łódź, Poland
Ivan Wilde
Affiliation:
Department of Mathematics, King's College, Strand, London WC2R 2LS
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Abstract

Quantum stochastic integrals are constructed using the non-commutative Lp-space theory of Haagerup. The existence and uniqueness of the solution to quantum stochastic differential equations driven by quasi-Wiener noises, or noises satisfying generalized standing hypotheses, is established as is the Markov behaviour of the solution. Various examples of the theory are discussed, and quantum Ornstein-Uhlenbeck processes are obtained as explicit solutions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 3 , November 1994 , pp. 535 - 553
Copyright
Copyright © Cambridge Philosophical Society 1994

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