Diffusive representation of N-th order fractional brownian motion

This paper describes an effort to give a different representation of a newly Introduced n-th order fractional Brownian motion (n-fBm). The new representation is called diffusive representation which has been successfully applied to the 1/f^α fractional noise. Thus this paper generalizes such representation to cover also n-fBm which is an extension to the ordinary fBm, due to the fact that the spectral properties of n-fBm cover larger range of parameter α. Different from 1/f^α case, the solution involves finite part concept of theory of distribution. The advantage of the proposed method on synthesizing sample of n-fBm is presented.