Quantum stochastic operator cocycles via associated semigroups

J. Martin Lindsay; Stephen J. Wills

doi:10.1017/S0305004106009923

Quantum stochastic operator cocycles via associated semigroups

J. Martin Lindsay
, Stephen J. Wills

School of Mathematical Sciences

Lancaster University

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

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.

Original language	English
Pages (from-to)	535-556
Number of pages	22
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	142
Issue number	3
DOIs	https://doi.org/10.1017/S0305004106009923
Publication status	Published - May 2007

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https://hdl.handle.net/10468/14811Licence: CC BY-NC-ND

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title = "Quantum stochastic operator cocycles via associated semigroups",

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.",

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AB - 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.

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JF - Mathematical Proceedings of the Cambridge Philosophical Society

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Quantum stochastic operator cocycles via associated semigroups

Abstract

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