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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d13b/d1391.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1391.

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Length: 10 pages
Date of creation: Jan 2003
Date of revision:
Publication status: Published in K. Athreya, M. Majumdar, M. Puri and E. Waymire, eds., Probability, Statistics and Their Applications: Papers in Honor of Rabi Bhattacharya, Vol. 41, Institute of Mathematical Statistics, 2003, pp. 285-292
Handle: RePEc:cwl:cwldpp:1391

Note: CFP 1115.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Brownian motion; fractional Brownian motion; fractional derivative; covariance functional; delta function; generalized derivative; generalized Gaussian process;

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Cited by:
  1. Zinde-Walsh, Victoria, 2008. "Kernel Estimation When Density May Not Exist," Econometric Theory, Cambridge University Press, vol. 24(03), pages 696-725, June.
  2. ZINDE-WALSH, Victoria, 2005. "Kernel Estimation when Density Does Not Exist," Cahiers de recherche 09-2005, Centre interuniversitaire de recherche en ├ęconomie quantitative, CIREQ.
  3. Victoria Zinde-Walsh, 2009. "Errors-In-Variables Models: A Generalized Functions Approach," Departmental Working Papers 2009-09, McGill University, Department of Economics.

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