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.

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",

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