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A matrix formulation of quantum stochastic calculus

Abstract:

We develop the theory of chaos spaces and chaos matrices. A chaos space is a Hilbert space with a fixed, countably-infinite, direct-sum decomposition. A chaos matrix between two chaos spaces is a doubly-infinite matrix of bounded operators which respects this decomposition. We study operators represented by such matrices, particularly with respect to self-adjointness. This theory is used to re-formulate the quantum stochastic calculus of Hudson and Parthasarathy. Integrals of chaos-matrix pr...

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Publication date:
1998
URN:
uuid:a0603234-3b3b-4832-a741-77778008d75f
Local pid:
oai:eprints.maths.ox.ac.uk:29

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