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Non-commutative stochastic distributions and applications to linear systems theory

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  • Alpay, Daniel
  • Salomon, Guy

Abstract

In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. Special inequalities which hold in this space allow to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.

Suggested Citation

  • Alpay, Daniel & Salomon, Guy, 2013. "Non-commutative stochastic distributions and applications to linear systems theory," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2303-2322.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:6:p:2303-2322
    DOI: 10.1016/j.spa.2013.02.005
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    References listed on IDEAS

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    1. Alpay, Daniel & Attia, Haim & Levanony, David, 2010. "On the characteristics of a class of Gaussian processes within the white noise space setting," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1074-1104, July.
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    Cited by:

    1. Ilwoo Cho & Palle E. T. Jorgensen, 2015. "Free W * -Dynamical Systems From p -Adic Number Fields and the Euler Totient Function," Mathematics, MDPI, vol. 3(4), pages 1-44, December.
    2. Jeremy Becnel & Ambar Sengupta, 2016. "Nuclear Space Facts, Strange and Plain," Mathematics, MDPI, vol. 4(4), pages 1-19, October.

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