CFDP 1391

Fractional Brownian Motion as a Differentiable Generalized Gaussian Process

Author(s): 

Publication Date: January 2003

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.

Keywords: 

Brownian motion, fractional Brownian motion, fractional derivative, covariance functional, delta function, generalized derivative, generalized Gaussian process

JEL Classification Codes: C32 Time Series Models