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.
|Number of pages||17|
|Publication status||Published - 1999|
|MoE publication type||A1 Journal article-refereed|
Norros, I., Valkeila, E., & Virtamo, J. (1999). An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. Bernoulli, 5(4), 571-587. https://projecteuclid.org/euclid.bj/1171899318