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

Ilkka Norros; Esko Valkeila; Jorma Virtamo

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

Ilkka Norros
, Esko Valkeila
, Jorma Virtamo

University of Helsinki
Helsinki University of Technology

Research output: Contribution to journal › Article › Scientific › peer-review

300 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 language	English
Pages (from-to)	571-587
Journal	Bernoulli
Volume	5
Issue number	4
Publication status	Published - 1999
MoE publication type	A1 Journal article-refereed

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Cite this

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title = "An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions",

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.",

author = "Ilkka Norros and Esko Valkeila and Jorma Virtamo",

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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.

M3 - Article

SN - 1350-7265

VL - 5

SP - 571

EP - 587

JO - Bernoulli

JF - Bernoulli

IS - 4

ER -

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

Abstract

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