An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions

Ilkka Norros, Esko Valkeila, Jorma Virtamo

    Research output: Contribution to journalArticleScientificpeer-review

    235 Citations (Scopus)

    Abstract

    The Radon-Nikodym derivative between a centred fractional Brownian motion Z and the same process with constant drift is derived by finding an integral transformation which changes Z to a process with independent increments. A representation of Z through a standard Brownian motion on a finite interval is given. The maximum-likelihood estimator of the drift and some other applications are presented.
    Original languageEnglish
    Pages (from-to)571-587
    JournalBernoulli
    Volume5
    Issue number4
    Publication statusPublished - 1999
    MoE publication typeA1 Journal article-refereed

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