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Publicação
On the relation between the fractional Brownian motion and the fractional derivatives
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Autores
Orientador(es)
Resumo(s)
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.
Descrição
Physics Letters A, vol. 372; Issue 7
Palavras-chave
Forward and backward fractional derivatives Generalised Cauchy derivative Liouville derivative Differintegration Central fractional derivatives Fractional stochastic process Fractional Brownian motion
Contexto Educativo
Citação
Editora
Elsevier B.V.