A stochastic Stinespring Theorem

Debashish Goswami; J. Martin Lindsay; Stephen J. Wills

doi:10.1007/PL00004453

A stochastic Stinespring Theorem

Debashish Goswami
, J. Martin Lindsay
, Stephen J. Wills

Indian Statistical Institute
University of Nottingham

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	647-673
Number of pages	27
Journal	Mathematische Annalen
Volume	319
Issue number	4
DOIs	https://doi.org/10.1007/PL00004453
Publication status	Published - 2001
Externally published	Yes

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title = "A stochastic Stinespring Theorem",

abstract = "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.",

author = "Debashish Goswami and Lindsay, \{J. Martin\} and Wills, \{Stephen J.\}",

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AU - Wills, Stephen J.

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AB - 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.

UR - https://www.scopus.com/pages/publications/0035607185

U2 - 10.1007/PL00004453

DO - 10.1007/PL00004453

M3 - Article

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SN - 0025-5831

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SP - 647

EP - 673

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 4

ER -

A stochastic Stinespring Theorem

Abstract

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