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

213 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
Number of pages17
JournalBernoulli
Volume5
Issue number4
Publication statusPublished - 1999
MoE publication typeA1 Journal article-refereed

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Fractional Brownian Motion
Processes with Independent Increments
Radon-Nikodym Derivative
Integral Transformation
Maximum Likelihood Estimator
Brownian motion
Interval
Standards

Cite this

Norros, Ilkka ; Valkeila, Esko ; Virtamo, Jorma. / An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. In: Bernoulli. 1999 ; Vol. 5, No. 4. pp. 571-587.
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An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. / Norros, Ilkka; Valkeila, Esko; Virtamo, Jorma.

In: Bernoulli, Vol. 5, No. 4, 1999, p. 571-587.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions

AU - Norros, Ilkka

AU - Valkeila, Esko

AU - Virtamo, Jorma

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

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EP - 587

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

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