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Quantum stochastic operator cocycles via associated semigroups

Published online by Cambridge University Press:  01 May 2007

J. MARTIN LINDSAY  and
STEPHEN J. WILLS
J. MARTIN LINDSAY
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF. e-mail: [email protected]
STEPHEN J. WILLS
Affiliation:
School of Mathematical Sciences, University College Cork, Cork, Ireland. e-mail: [email protected]
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Abstract

A recent characterisation of Fock-adapted contraction operator stochastic cocycles on a Hilbert space, in terms of their associated semigroups, yields a general principle for the construction of such cocycles by approximation of their stochastic generators. This leads to new existence results for quantum stochastic differential equations. We also give necessary and sufficient conditions for a cocycle to satisfy such an equation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 3 , May 2007 , pp. 535 - 556
Copyright
Copyright © Cambridge Philosophical Society 2007

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