Fractional Brownian Motion as a Differentiable Generalized Gaussian Process
AbstractBrownian 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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Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1391.
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
Note: CFP 1115.
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-02-03 (All new papers)
- NEP-ECM-2003-02-10 (Econometrics)
- NEP-ETS-2003-02-03 (Econometric Time Series)
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"Errors-in-Variables Models : A Generalized Functions Approach,"
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- 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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