DCT and Eigenvectors of Covariance of 1st and 2nd order Discrete fractional Brownian motion

This paper establishes connection between discrete cosine transform (DCT) and 1st and 2nd order discrete-time fractional Brownian motion process. It is proved that the eigenvectors of the auto-covariance matrix of a 1st and 2nd order discrete-time fractional Brownian motion can be approximated by DCT basis vectors in the asymptotic sense. Perturbation in eigenvectors from DCT basis vectors is modeled using the analytic perturbation theory of linear operators.