Title

Fractional Brownian Motion as a Differentiable Generalized Gaussian Process

Document Type

Discussion Paper

Publication Date

1-1-2003

CFDP Number

1391

CFDP Pages

10

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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