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.
|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|
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