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Diagonal versions and quantum stochastic integrals on the symmetric Fock space with nonadapted integrands
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  • Published: October 1998

Diagonal versions and quantum stochastic integrals on the symmetric Fock space with nonadapted integrands

  • Volkmar Liebscher1 

Probability Theory and Related Fields volume 112, pages 255–295 (1998)Cite this article

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Abstract.

We develop a quantum stochastic calculus for nonadapted processes and the three standard integrators on the symmetric Fock space over an arbitrary Polish space. The integrable processes are restricted to a class of operators which possess some kernel description. Our approach is mainly based on the concept of diagonalized versions [16]. In the case of the real line we consider connections to the usual stochastic and quantum stochastic calculi and derive Itô-formulae. Besides the standard integrals with two integrands and one integrator these formulae lead to a new type of quantum stochastic integrals which has two integrators and three integrands.

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  1. Institut für Angewandte Mathematik, Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, D-07740 Jena, Germany. e-mail: liebscher@minet.uni-jena.de, , , , , , DE

    Volkmar Liebscher

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  1. Volkmar Liebscher
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Received: 16 June 1997/Revised version: 1 April 1998

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Liebscher, V. Diagonal versions and quantum stochastic integrals on the symmetric Fock space with nonadapted integrands. Probab Theory Relat Fields 112, 255–295 (1998). https://doi.org/10.1007/s004400050190

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  • Issue Date: October 1998

  • DOI: https://doi.org/10.1007/s004400050190

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  • Mathematics Subject Classification (1991): 81S25
  • 60H05
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