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Fractional Brownian Motion as a Differentiable Generalized Gaussian Process

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Abstract

Brownian motion can be characterized as a generalized random process and, as such, has a generalized derivative whose covariance functional is the delta function. In a similar fashion, fractional Brownian motion can be interpreted as a generalized random process and shown to possess a generalized derivative. The resulting process is a generalized Gaussian process with mean functional zero and covariance functional that can be interpreted as a fractional integral or fractional derivative of the delta-function.

Suggested Citation

  • Victoria Zinde-Walsh & Peter C.B. Phillips, 2003. "Fractional Brownian Motion as a Differentiable Generalized Gaussian Process," Cowles Foundation Discussion Papers 1391, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1391
    Note: CFP 1115.
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d13/d1391.pdf
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    Cited by:

    1. ZINDE-WALSH, Victoria, 2005. "Kernel Estimation when Density Does Not Exist," Cahiers de recherche 09-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Zinde-Walsh, Victoria, 2008. "Kernel Estimation When Density May Not Exist," Econometric Theory, Cambridge University Press, vol. 24(3), pages 696-725, June.
    3. ZINDE-WALSH, Victoria, 2007. "Errors-in-Variables Models : A Generalized Functions Approach," Cahiers de recherche 14-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

    More about this item

    Keywords

    Brownian motion; fractional Brownian motion; fractional derivative; covariance functional; delta function; generalized derivative; generalized Gaussian process;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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