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|Title:||On the relation between the fractional Brownian motion and the fractional derivatives|
Batista, A. G.
|Keywords:||Forward and backward fractional derivatives|
Generalised Cauchy derivative
Central fractional derivatives
Fractional stochastic process
Fractional Brownian motion
|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|
|Appears in Collections:||FCT: DEE - Artigos em revista internacional com arbitragem científica|
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