## 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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