Fractional Brownian Motion as a Differentiable Generalized Gaussian Process

Victoria Zinde-Walsh and Peter Phillips

No 1391, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 (search for similar items in EconPapers)
JEL-codes: C32 (search for similar items in EconPapers)
Pages: 10 pages
Date: 2003-01
New Economics Papers: this item is included in nep-ecm and nep-ets
Note: CFP 1115.
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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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