Cottone, Giulio; di Paola, Mario; Santoro, Roberta A novel exact representation of stationary colored Gaussian processes (fractional differential approach). (English) Zbl 1187.82043 J. Phys. A, Math. Theor. 43, No. 8, Article ID 085002, 16 p. (2010). Summary: A novel representation of functions, called generalized Taylor form, is applied to the filtering of white noise processes. It is shown that every Gaussian colored noise can be expressed as the output of a set of linear fractional stochastic differential equations whose solution is a weighted sum of fractional Brownian motions. The exact form of the weighting coefficients is given and it is shown that it is related to the fractional moments of the target spectral density of the colored noise. Cited in 20 Documents MSC: 82B31 Stochastic methods applied to problems in equilibrium statistical mechanics 60J65 Brownian motion 60G22 Fractional processes, including fractional Brownian motion 34A08 Fractional ordinary differential equations Keywords:Gaussian white noise; time series model PDFBibTeX XMLCite \textit{G. Cottone} et al., J. Phys. A, Math. Theor. 43, No. 8, Article ID 085002, 16 p. (2010; Zbl 1187.82043) Full Text: DOI arXiv