On the prediction of fractional brownian motion

Gustaf Gripenberg, Ilkka Norros

Research output: Contribution to journalArticleScientificpeer-review

124 Citations (Scopus)

Abstract

Integration with respect to the fractional Brownian motion Z with Hurst parameter H ∈ (1/2, 1) is discussed. The predictor E[Za ∣ Zs, s ∈ (-T, 0)] is represented as an integral with respect to Z, solving a weakly singular integral equation for the prediction weight function.
Original languageEnglish
Pages (from-to)400-410
Number of pages11
JournalJournal of Applied Probability
Volume33
Issue number2
DOIs
Publication statusPublished - 1996
MoE publication typeA1 Journal article-refereed

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Hurst Parameter
Fractional Brownian Motion
Singular Integral Equation
Weight Function
Predictors
Prediction
Fractional Brownian motion
Integral equations
Integral

Cite this

Gripenberg, Gustaf ; Norros, Ilkka. / On the prediction of fractional brownian motion. In: Journal of Applied Probability. 1996 ; Vol. 33, No. 2. pp. 400-410.
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On the prediction of fractional brownian motion. / Gripenberg, Gustaf; Norros, Ilkka.

In: Journal of Applied Probability, Vol. 33, No. 2, 1996, p. 400-410.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Gripenberg, Gustaf

AU - Norros, Ilkka

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AB - Integration with respect to the fractional Brownian motion Z with Hurst parameter H ∈ (1/2, 1) is discussed. The predictor E[Za ∣ Zs, s ∈ (-T, 0)] is represented as an integral with respect to Z, solving a weakly singular integral equation for the prediction weight function.

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DO - 10.2307/3215063

M3 - Article

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JO - Journal of Applied Probability

JF - Journal of Applied Probability

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