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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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