A Geometrical Study of the Bivariate Fractional Gaussian Noise

We study the stochastic properties of the bivariate fractional Gaussian noise based on a polarization spectral analysis. The originality of the approach consist in the particular attention given to geometric features, achieved by the use of spectral quantities named Stokes parameters. Explicit expressions for these parameters are provided for the bivariate fractional noise. A special attention is given to the notion of degree of polarization, which allows to provide the synthesis of the fractional Gaussian noise as the sum of polarized and unpolarized processes.