A stochastic Stinespring Theorem

Goswami, Debashish ; Lindsay, J. Martin ; Wills, Stephen J. (2001) A stochastic Stinespring Theorem Mathematische Annalen, 319 (4). pp. 647-673. ISSN 0025-5831

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Official URL: http://link.springer.com/article/10.1007/PL0000445...

Related URL: http://dx.doi.org/10.1007/PL00004453


Completely positive Markovian cocycles on a von Neumann algebra, adapted to a Fock filtration, are realised as conjugations of *-homomorphic Markovian cocycles. The conjugating processes are affiliated to the algebra, and are governed by quantum stochastic differential equations whose coefficients evolve according to the *-homomorphic process. Some perturbation theory for quantum stochastic flows is developed in order to achieve the above Stinespring decomposition.

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