Prediction law of fractional Brownian motion

Tommi Sottinen*, Lauri Viitasaari

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)155-166
Number of pages12
JournalStatistics and Probability Letters
Publication statusPublished - 1 Oct 2017
MoE publication typeA1 Journal article-refereed


  • Fractional Brownian motion
  • Prediction
  • Regular conditional law


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