TY: JOUR
T1 - On the relation between the fractional Brownian motion and the fractional derivatives
A1 - Ortigueira, M.D.
A1 - Batista, A. G.
N2 - 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.
UR - http://run.unl.pt/handle/10362/2416
Y1 - 2008
PB - Elsevier B.V.