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.