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Prediction law of fractional Brownian motion

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  • Sottinen, Tommi
  • Viitasaari, Lauri

Abstract

We calculate the regular conditional future law of the fractional Brownian motion with index H∈(0,1) conditioned on its past. We show that the conditional law is continuous with respect to the conditioning path. We investigate the path properties of the conditional process and the asymptotic behavior of the conditional covariance.

Suggested Citation

  • Sottinen, Tommi & Viitasaari, Lauri, 2017. "Prediction law of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 155-166.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:155-166
    DOI: 10.1016/j.spl.2017.05.006
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    References listed on IDEAS

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    1. Duncan, T.E., 2006. "Prediction for some processes related to a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 128-134, January.
    2. Sottinen, Tommi & Yazigi, Adil, 2014. "Generalized Gaussian bridges," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3084-3105.
    3. Jost, Céline, 2006. "Transformation formulas for fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1341-1357, October.
    4. Azmoodeh, Ehsan & Sottinen, Tommi & Viitasaari, Lauri & Yazigi, Adil, 2014. "Necessary and sufficient conditions for Hölder continuity of Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 230-235.
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    Citations

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    Cited by:

    1. Shokrollahi, Foad & Sottinen, Tommi, 2017. "Hedging in fractional Black–Scholes model with transaction costs," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 85-91.
    2. Raul Merino & Jan Posp'iv{s}il & Tom'av{s} Sobotka & Tommi Sottinen & Josep Vives, 2019. "Decomposition formula for rough Volterra stochastic volatility models," Papers 1906.07101, arXiv.org, revised Aug 2019.
    3. Tommi Sottinen & Lauri Viitasaari, 2017. "Conditional-Mean Hedging Under Transaction Costs in Gaussian Models," Papers 1708.03242, arXiv.org.
    4. Tommi Sottinen & Lauri Viitasaari, 2018. "Conditional-Mean Hedging Under Transaction Costs In Gaussian Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-15, March.
    5. Maleki Almani, Hamidreza & Shokrollahi, Foad & Sottinen, Tommi, 2024. "Prediction of Gaussian Volterra processes with compound Poisson jumps," Statistics & Probability Letters, Elsevier, vol. 208(C).

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