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Fractional Brownian Motion as a Differentiable Generalized Gaussian Process

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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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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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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