The Ito-Clifford Wong-Zakai Integrals and Martingale Representation

    Research output: Chapter in Book/Report/Conference proceedingConference contribution


    Classical stochastic integration is based upon a probability space involving a filtration of sigma-algebras. This construction lends itself to non-commutative quantum analogues based for example, on a Hilbert space, a filtration of Von Neumann algebras and gage. We recall a non-commutative construction for the two parameter case, these being integrals in the plane, resulting in type one and type two stochastic integrals which are orthogonal, centred L2 - martingales, obeying isometry properties and develop the construction to obtain an Ito-Clifford Wong-Zakai martingalerepresentation.
    Original languageEnglish
    Title of host publicationFoundations of Probability and Physics - 4
    EditorsGuillaume Adenier, Christopher A. Fuchs, Andrei Yu Khrennikov
    Place of PublicationNew York
    PublisherAmerican Institute of Physics (AIP)
    ISBN (Electronic)9780735403918
    Publication statusPublished - 2007

    Publication series

    NameFoundations of Probability and Physics
    PublisherAmerican Institute of Physics


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