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On the prediction of fractional Brownian motion

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Gustaf Gripenberg  and
Ilkka Norros
Gustaf Gripenberg*
Affiliation:
University of Helsinki
Ilkka Norros*
Affiliation:
VTT Information Technology
*
∗Postal address: University of Helsinki, Department of Mathematics, P.O. Box 4, 00014 University of Helsinki, Finland. e-mail:gustaf.gripenberg@helsinki.fi
∗∗Postal address: VTT Information Technology, Telecommunications, P.O. Box 1202, 02044 VTT, Finland. e-mail:ilkka.norros@vtt.fi
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Abstract

Integration with respect to the fractional Brownian motion Z with Hurst parameter is discussed. The predictor is represented as an integral with respect to Z, solving a weakly singular integral equation for the prediction weight function.

Keywords

FRACTIONAL BROWNIAN MOTIONPREDICTIONSTOCHASTIC INTEGRATION

MSC classification

Primary: 60G25: Prediction theory
Secondary: 60G15: Gaussian processes 60G18: Self-similar processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 400 - 410
Copyright
Copyright © Applied Probability Trust 1996 

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