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.