On multi-dimensional markovian cocycles

Accardi, Luigi; Journé, Jean-Lin; Lindsay, J. Martin

doi:10.1007/bfb0083543

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Cited by 27 publications

(45 citation statements)

References 7 publications

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“…We expect that the integral representation of quantum martingales have applications in Markovian cocycles [1,4,13]. Further study is now in progress.…”

Section: Introductionmentioning

confidence: 94%

Stochastic integral representations of quantum martingales on multiple Fock space

2006

Proc. Indian Acad. Sci. (Math. Sci.)

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“…We expect that the integral representation of quantum martingales have applications in Markovian cocycles [1,4,13]. Further study is now in progress.…”

Section: Introductionmentioning

confidence: 94%

Stochastic integral representations of quantum martingales on multiple Fock space

2006

Proc. Indian Acad. Sci. (Math. Sci.)

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“…These papers extend to field the notion of quantum Markov state introduced in [3] as a sub-class of the quantum Markov chains introduced in [1].…”

Section: Introductionmentioning

confidence: 99%

Phase transitions for XY-model on the Cayley tree of order three in quantum Markov chain scheme

Mukhamedov

Saburov

2011

Comptes Rendus. Mathématique

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“…For situations where the expectation semigroup is not norm continuous, the characterization problem is discussed in [5,1]. In [10,11], by extended semigroup methods, Lindsay and Wills have studied such problems for Fock adapted contractive operator cocycles and completely positive cocyles.…”

Section: §1 Introductionmentioning

confidence: 99%

Unitary Processes with Independent Increments and Representations of Hilbert Tensor Algebras

Sahu¹,

Schürmann²,

Sinha³

2009

Publ. Res. Inst. Math. Sci.

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The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson-Parthasarathy flow. §1. IntroductionIn the framework of the theory of quantum stochastic calculus developed by pioneering work of Hudson and Parthasarathy [6], quantum stochastic differential equations (qsde) of the form

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On multi-dimensional markovian cocycles

Cited by 27 publications

References 7 publications

Stochastic integral representations of quantum martingales on multiple Fock space

Stochastic integral representations of quantum martingales on multiple Fock space

Phase transitions for XY-model on the Cayley tree of order three in quantum Markov chain scheme

Unitary Processes with Independent Increments and Representations of Hilbert Tensor Algebras

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