The Ito-Clifford Wong-Zakai Integrals and Martingale Representation

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

Abstract

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)
Pages407-411
Volume889
ISBN (Electronic)9780735403918
Publication statusPublished - 2007

Publication series

NameFoundations of Probability and Physics
PublisherAmerican Institute of Physics

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