Gripenberg, Gustaf; Norros, Ilkka On the prediction of fractional Brownian motion. (English) Zbl 0861.60049 J. Appl. Probab. 33, No. 2, 400-410 (1996). Integration with respect to the fractional Brownian motion \(Z\) with self-similar (Hurst, fractional) parameter \(H\in(0.5, 1)\) is discussed. Some properties of stochastic integrals are given. The explicit expression for the predictors \(E(Z_a\mid Z_s, s\in (-T,0])\), \(a\geq 0\), \(T>0\), is given for positively correlated fractional Brownian motion. Reviewer: N.Leonenko (Kiev) Cited in 1 ReviewCited in 65 Documents MSC: 60G25 Prediction theory (aspects of stochastic processes) 60G18 Self-similar stochastic processes 60G15 Gaussian processes 62M20 Inference from stochastic processes and prediction Keywords:fractional Brownian motion; stochastic integration; prediction PDFBibTeX XMLCite \textit{G. Gripenberg} and \textit{I. Norros}, J. Appl. Probab. 33, No. 2, 400--410 (1996; Zbl 0861.60049) Full Text: DOI