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On the characteristics of a class of Gaussian processes within the white noise space setting

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  • Alpay, Daniel
  • Attia, Haim
  • Levanony, David

Abstract

Using the white noise space framework, we construct and study a class of Gaussian processes with stationary increments, which include as particular cases the Brownian and fractional Brownian motions. The derivative processes are computed using Hida's theory of stochastic distributions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:7:p:1074-1104
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    References listed on IDEAS

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    1. Robert J. Elliott & John Van Der Hoek, 2003. "A General Fractional White Noise Theory And Applications To Finance," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 301-330, April.
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    Cited by:

    1. Daniel Alpay & Palle Jorgensen & David Levanony, 2017. "On the Equivalence of Probability Spaces," Journal of Theoretical Probability, Springer, vol. 30(3), pages 813-841, September.
    2. 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.
    3. Daniel Alpay & Palle Jorgensen, 2022. "mu-Brownian Motion, Dualities, Diffusions, Transforms, and Reproducing Kernel Hilbert Spaces," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2757-2783, December.

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