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    Rights statement: The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 409 (2), 2013, © ELSEVIER.

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Sesquilinear quantum stochastic analysis in Banach space

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Sesquilinear quantum stochastic analysis in Banach space. / Lindsay, Martin; Das, Bata Krishna; Tripak, Orawan.
In: Journal of Mathematical Analysis and Applications, Vol. 409, No. 2, 15.01.2014, p. 1031-1051.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Lindsay, M, Das, BK & Tripak, O 2014, 'Sesquilinear quantum stochastic analysis in Banach space', Journal of Mathematical Analysis and Applications, vol. 409, no. 2, pp. 1031-1051. https://doi.org/10.1016/j.jmaa.2013.01.067

APA

Lindsay, M., Das, B. K., & Tripak, O. (2014). Sesquilinear quantum stochastic analysis in Banach space. Journal of Mathematical Analysis and Applications, 409(2), 1031-1051. https://doi.org/10.1016/j.jmaa.2013.01.067

Vancouver

Lindsay M, Das BK, Tripak O. Sesquilinear quantum stochastic analysis in Banach space. Journal of Mathematical Analysis and Applications. 2014 Jan 15;409(2):1031-1051. Epub 2013 Sept 19. doi: 10.1016/j.jmaa.2013.01.067

Author

Lindsay, Martin ; Das, Bata Krishna ; Tripak, Orawan. / Sesquilinear quantum stochastic analysis in Banach space. In: Journal of Mathematical Analysis and Applications. 2014 ; Vol. 409, No. 2. pp. 1031-1051.

Bibtex

@article{e914df3207374a62a189998d1208612e,
title = "Sesquilinear quantum stochastic analysis in Banach space",
abstract = "A theory of quantum stochastic processes in Banach space is initiated. The processes considered here consist of Banach space valued sesquilinear maps. We establish an existence and uniqueness theorem for quantum stochastic differential equations in Banach modules, show that solutions in unital Banach algebras yield stochastic cocycles, give sufficient conditions for a stochastic cocycle to satisfy such an equation, and prove a stochastic Lie–Trotter product formula. The theory is used to extend, unify and refine standard quantum stochastic analysis through different choices of Banach space, of which there are three paradigm classes: spaces of bounded Hilbert space operators, operator mapping spaces and duals of operator space coalgebras. Our results provide the basis for a general theory of quantum stochastic processes in operator spaces, of which L{\'e}vy processes on compact quantum groups is a special case.",
keywords = "Quantum stochastic differential equation , Quantum Wiener integral, Quantum stochastic cocycle, Trotter product formula",
author = "Martin Lindsay and Das, {Bata Krishna} and Orawan Tripak",
note = "The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 409 (2), 2013, {\textcopyright} ELSEVIER.",
year = "2014",
month = jan,
day = "15",
doi = "10.1016/j.jmaa.2013.01.067",
language = "English",
volume = "409",
pages = "1031--1051",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "2",

}

RIS

TY - JOUR

T1 - Sesquilinear quantum stochastic analysis in Banach space

AU - Lindsay, Martin

AU - Das, Bata Krishna

AU - Tripak, Orawan

N1 - The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 409 (2), 2013, © ELSEVIER.

PY - 2014/1/15

Y1 - 2014/1/15

N2 - A theory of quantum stochastic processes in Banach space is initiated. The processes considered here consist of Banach space valued sesquilinear maps. We establish an existence and uniqueness theorem for quantum stochastic differential equations in Banach modules, show that solutions in unital Banach algebras yield stochastic cocycles, give sufficient conditions for a stochastic cocycle to satisfy such an equation, and prove a stochastic Lie–Trotter product formula. The theory is used to extend, unify and refine standard quantum stochastic analysis through different choices of Banach space, of which there are three paradigm classes: spaces of bounded Hilbert space operators, operator mapping spaces and duals of operator space coalgebras. Our results provide the basis for a general theory of quantum stochastic processes in operator spaces, of which Lévy processes on compact quantum groups is a special case.

AB - A theory of quantum stochastic processes in Banach space is initiated. The processes considered here consist of Banach space valued sesquilinear maps. We establish an existence and uniqueness theorem for quantum stochastic differential equations in Banach modules, show that solutions in unital Banach algebras yield stochastic cocycles, give sufficient conditions for a stochastic cocycle to satisfy such an equation, and prove a stochastic Lie–Trotter product formula. The theory is used to extend, unify and refine standard quantum stochastic analysis through different choices of Banach space, of which there are three paradigm classes: spaces of bounded Hilbert space operators, operator mapping spaces and duals of operator space coalgebras. Our results provide the basis for a general theory of quantum stochastic processes in operator spaces, of which Lévy processes on compact quantum groups is a special case.

KW - Quantum stochastic differential equation

KW - Quantum Wiener integral

KW - Quantum stochastic cocycle

KW - Trotter product formula

U2 - 10.1016/j.jmaa.2013.01.067

DO - 10.1016/j.jmaa.2013.01.067

M3 - Journal article

VL - 409

SP - 1031

EP - 1051

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -