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Quantum Stochastic Integral Representations on Interacting Fock Space

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Abstract

A quantum stochastic integration theory on interacting Fock space (IFS) has been established in Crismale (Commun Stoch Anal 1(2):321–341, 2007). In this paper, we firstly put forward a family of left–right conditional expectations \(E_{t}\), for \(t\in R_{+}\), on the von Neumann algebra \(\mathcal {V}\) generated by the creation, annihilation and gauge operators acting on IFS over \({L}^{2}(R_{+})\). Next, we develop a generalized quantum stochastic integral. Finally, we prove that any process \(\Xi \in (\mathcal {V}_{t})_{t\in R_{+}}\) admits a quantum stochastic integral representation.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Yuanbao Kang & Caishi Wang

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  1. Yuanbao Kang
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  2. Caishi Wang
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Correspondence to Yuanbao Kang.

Additional information

Research supported by the National Natural Science Foundation of China (Grant No. 11061032) and Natural Science Foundation of Gansu Province (Grant No 0710RJZA106).

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Kang, Y., Wang, C. Quantum Stochastic Integral Representations on Interacting Fock Space. J Theor Probab 28, 1007–1027 (2015). https://doi.org/10.1007/s10959-013-0537-5

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  • DOI: https://doi.org/10.1007/s10959-013-0537-5

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