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Prediction law of fractional Brownian motion

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2017Embargo end date: 01 Jan 2016 Finland Publisher:Elsevier BVJournal:Statistics & Probability Letters, volume 129, pages 155-166 (issn: 0167-7152,

Authors: Viitasaari; Lauri; Sottinen, Tommi;

doi: 10.1016/j.spl.2017.05.006 , 10.48550/arxiv.1610.02900

arXiv: http://arxiv.org/abs/1610.02900

Prediction law of fractional Brownian motion

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Abstract

We calculate the regular conditional future law of the fractional Brownian motion with index $H\in(0,1)$ 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.

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Finland

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Keywords

ta112, ta111, Probability (math.PR), fractional Brownian motion, regular conditional law, Talousmatematiikka, prediction, Fractional Brownian motion, Regular conditional law, FOS: Mathematics, 60G22, 60G25, Prediction, Mathematics - Probability

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