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Title: On the relation between the fractional Brownian motion and the fractional derivatives
Author: Ortigueira, M.D.
Batista, A. G.
Keywords: Forward and backward fractional derivatives
Generalised Cauchy derivative
Liouville derivative
Central fractional derivatives
Fractional stochastic process
Fractional Brownian motion
Issue Date: Aug-2008
Publisher: Elsevier B.V.
Abstract: The definition and simulation of fractional Brownian motion are considered from the point of view of a set of coherent fractional derivative definitions. To do it, two sets of fractional derivatives are considered: (a) the forward and backward and (b) the central derivatives, together with two representations: generalised difference and integral. It is shown that for these derivatives the corresponding autocorrelation functions have the same representations. The obtained results are used to define a fractional noise and, from it, the fractional Brownian motion. This is studied. The simulation problem is also considered.
Description: Physics Letters A, vol. 372; Issue 7
ISSN: 0375-9601
Appears in Collections:FCT: DEE - Artigos em revista internacional com arbitragem científica

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