An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. (English) Zbl 0955.60034

Norros, Ilkka; Valkeila, Esko; Virtamo, Jorma

Bernoulli 5, No. 4, 571-587 (1999).

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.

Reviewer: Heinrich von Weizsäcker (Kaiserslautern)

MSC:

60G15	Gaussian processes
60G25	Prediction theory (aspects of stochastic processes)
60G30	Continuity and singularity of induced measures
62M99	Inference from stochastic processes

Keywords:

fractional Brownian motion; Gaussian martingales; Girsanov density; beta function; maximum likelihood