Singularity spectra of fractional Brownian motions as a multi-fractal

Fractional Brownian motion acts as a random process with statistical self-similarity in time and self-affinity in shape. From these properties, the complicated patterns can be suitably represented by it with a minimal parameter and less memory. By considering its statistical property through the power spectrum density we can see that this process is not stationary, even though its differential motion is stationary. So in this paper, by taking the wavelet transfom instead of Fourier transformation we investigate its multi-fractal spectrum as a multi-fractal model.