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

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.


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