Identification of the multiscale fractional Brownian motion with biomechanical applications
Statistics Theory
2007-06-13 v1 Statistics Theory
Abstract
In certain applications, for instance biomechanics, turbulence, finance, or Internet traffic, it seems suitable to model the data by a generalization of a fractional Brownian motion for which the Hurst parameter is depending on the frequency as a piece-wise constant function. These processes are called multiscale fractional Brownian motions. In this contribution, we provide a statistical study of the multiscale fractional Brownian motions. We develop a method based on wavelet analysis. By using this method, we find initially the frequency changes, then we estimate the different parameters and afterwards we test the goodness-of-fit. Lastly, we give the numerical algorithm. Biomechanical data are then studied with these new tools.
Keywords
Cite
@article{arxiv.math/0701873,
title = {Identification of the multiscale fractional Brownian motion with biomechanical applications},
author = {Jean-Marc Bardet and Pierre Bertrand},
journal= {arXiv preprint arXiv:math/0701873},
year = {2007}
}