Identification of the multiscale fractional Brownian motion with biomechanical applications

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 (FBM) for which the Hurst parameter H depends on the frequency as a piece-wise constant function. These processes are called multiscale fractional Brownian motions. In this article, we provide a statistical study of the multiscale fractional Brownian motions. We developed a method based on wavelet analysis. By using this method, we calculated the frequency changes, estimated the different parameters, tested the goodness-of-fit and gave the numerical algorithm. Biomechanical data are then studied with these new tools.