On the relation between the fractional Brownian motion and the fractional deriv...

• Author(s): Ortigueira, M.D. ; Batista, A. G.
• Date: 2008
• Persistent ID: http://hdl.handle.net/10362/2416
• Origin: Repositório Institucional da UNL
• Subject(s): Forward and backward fractional derivatives; Generalised Cauchy derivative; Liouville derivative; Differintegration; Central fractional derivatives; Fractional stochastic process; Fractional Brownian motion
• Document Type: Article
• Language: English

Description

Physics Letters A, vol. 372; Issue 7 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.