Home > Research > Publications & Outputs > Quantum stochastic convolution cocycles III

Electronic data

  • 2010vii08revisedQSCC3

    Rights statement: The original publication is available at www.link.springer.com

    Submitted manuscript, 253 KB, PDF document

Links

Text available via DOI:

View graph of relations

Quantum stochastic convolution cocycles III

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published

Standard

Quantum stochastic convolution cocycles III. / Lindsay, J. Martin; Skalski, Adam G.
In: Mathematische Annalen, Vol. 352, No. 4, 04.2012, p. 779-804.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

APA

Vancouver

Lindsay JM, Skalski AG. Quantum stochastic convolution cocycles III. Mathematische Annalen. 2012 Apr;352(4):779-804. doi: 10.1007/s00208-011-0656-1

Author

Lindsay, J. Martin ; Skalski, Adam G. / Quantum stochastic convolution cocycles III. In: Mathematische Annalen. 2012 ; Vol. 352, No. 4. pp. 779-804.

Bibtex

@article{7c0eb0aab24d44a5a98d2ae8a1e023c5,
title = "Quantum stochastic convolution cocycles III",
abstract = "The theory of quantum Levy processes on a compact quantum group, and more generally quantum stochastic convolution cocycles on a C*-bialgebra, is extended to locally compact quantum groups and multiplier C*-bialgebras. Strict extension results obtained by Kustermans, and automatic strictness properties developed here, are exploited to obtain existence and uniqueness for coalgebraic quantum stochastic differential equations in this setting. Working in the universal enveloping von Neumann bialgebra, the stochastic generators of Markov-regular, completely positive, respectively *-homomorphic, quantum stochastic convolution cocycles are characterised. Every Markov-regular quantum Levy process on a multiplier C*-bialgebra is shown to be equivalent to one governed by a quantum stochastic differential equation, and the generating functionals of norm-continuous convolution semigroups on a multiplier C*-bialgebra are characterised. Applying a recent result of Belton's, we give a thorough treatment of the approximation of quantum stochastic convolution cocycles by quantum random walks. ",
author = "Lindsay, {J. Martin} and Skalski, {Adam G.}",
note = "The original publication is available at www.link.springer.com",
year = "2012",
month = apr,
doi = "10.1007/s00208-011-0656-1",
language = "English",
volume = "352",
pages = "779--804",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer New York",
number = "4",

}

RIS

TY - JOUR

T1 - Quantum stochastic convolution cocycles III

AU - Lindsay, J. Martin

AU - Skalski, Adam G.

N1 - The original publication is available at www.link.springer.com

PY - 2012/4

Y1 - 2012/4

N2 - The theory of quantum Levy processes on a compact quantum group, and more generally quantum stochastic convolution cocycles on a C*-bialgebra, is extended to locally compact quantum groups and multiplier C*-bialgebras. Strict extension results obtained by Kustermans, and automatic strictness properties developed here, are exploited to obtain existence and uniqueness for coalgebraic quantum stochastic differential equations in this setting. Working in the universal enveloping von Neumann bialgebra, the stochastic generators of Markov-regular, completely positive, respectively *-homomorphic, quantum stochastic convolution cocycles are characterised. Every Markov-regular quantum Levy process on a multiplier C*-bialgebra is shown to be equivalent to one governed by a quantum stochastic differential equation, and the generating functionals of norm-continuous convolution semigroups on a multiplier C*-bialgebra are characterised. Applying a recent result of Belton's, we give a thorough treatment of the approximation of quantum stochastic convolution cocycles by quantum random walks.

AB - The theory of quantum Levy processes on a compact quantum group, and more generally quantum stochastic convolution cocycles on a C*-bialgebra, is extended to locally compact quantum groups and multiplier C*-bialgebras. Strict extension results obtained by Kustermans, and automatic strictness properties developed here, are exploited to obtain existence and uniqueness for coalgebraic quantum stochastic differential equations in this setting. Working in the universal enveloping von Neumann bialgebra, the stochastic generators of Markov-regular, completely positive, respectively *-homomorphic, quantum stochastic convolution cocycles are characterised. Every Markov-regular quantum Levy process on a multiplier C*-bialgebra is shown to be equivalent to one governed by a quantum stochastic differential equation, and the generating functionals of norm-continuous convolution semigroups on a multiplier C*-bialgebra are characterised. Applying a recent result of Belton's, we give a thorough treatment of the approximation of quantum stochastic convolution cocycles by quantum random walks.

U2 - 10.1007/s00208-011-0656-1

DO - 10.1007/s00208-011-0656-1

M3 - Journal article

VL - 352

SP - 779

EP - 804

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 4

ER -