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Quantum stochastic calculus with maximal operator domains.

Lindsay, J. Martin and Attal, Stéphane (2004) Quantum stochastic calculus with maximal operator domains. The Annals of Probability, 32 (1a). pp. 488-529.

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    Abstract

    Quantum stochastic calculus is extended in a new formulation in which its stochastic integrals achieve their natural and maximal domains. Operator adaptedness, conditional expectations and stochastic integrals are all defined simply in terms of the orthogonal projections of the time filtration of Fock space, together with sections of the adapted gradient operator. Free from exponential vector domains, our stochastic integrals may be satisfactorily composed yielding quantum Itô formulas for operator products as sums of stochastic integrals. The calculus has seen two reformulations since its discovery—one closely related to classical Itô calculus; the other to noncausal stochastic analysis and Malliavin calculus. Our theory extends both of these approaches and may be viewed as a synthesis of the two. The main application given here is existence and uniqueness for the Attal–Meyer equations for implicit definition of quantum stochastic integrals.

    Item Type: Article
    Journal or Publication Title: The Annals of Probability
    Additional Information: RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
    Uncontrolled Keywords: Quantum stochastic ; Fock space ; Itô calculus ; noncausal ; chaotic representation property ; Malliavin calculus ; noncommutative probability
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 2380
    Deposited By: ep_importer
    Deposited On: 01 Apr 2008 11:25
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 13:14
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/2380

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