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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.

##### MSC:
 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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