Quantum stochastic operator cocycles via associated semigroups

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 qu...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 2007-05, Vol.142 (3), p.535-556
Main Authors: LINDSAY, J. MARTIN, WILLS, STEPHEN J.
Format: Article
Language:English
Subjects:
Differential equations
Mathematics
Physics
Quantum theory
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Summary: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.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004106009923