SPECTRAL REPRESENTATION OF FRACTIONAL BROWNIAN-MOTION IN N-DIMENSIONSAND ITS PROPERTIES

Fractional Brownian motion (fBm) provides a useful model for processes with strong long-term dependence, such as 1/f(beta) spectral behavior . However, fBm's are nonstationary processes so that the interpretatio n of such a spectrum is still a matter of speculation. To facilitate t he study of this problem, another model is provided for the constructi on of fBm from a white-noise-like process by means of a stochastic or Ita integral in frequency of a stationary uncorrelated random process. Also a generalized power spectrum of the nonstationary fBm process is defined. This new approach to fBm can be used to compute all of the c orrelations, power spectra, and other properties of fBm. In this paper , a number of these fBm properties are developed from this model such as the T-H law of scaling, the power law of fractional order, the corr elation of two arbitrary fBm's, and the evaluation of the fractal dime nsion under various transformations. This new treatment of fBm using a spectral representation is extended also, for the first time, to two or more topological dimensions in order to analyze the features of iso tropic n-dimensional fBm.