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On the prediction of fractional Brownian motion. (English) Zbl 0861.60049

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)

MSC:

60G25 Prediction theory (aspects of stochastic processes)
60G18 Self-similar stochastic processes
60G15 Gaussian processes
62M20 Inference from stochastic processes and prediction
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