Spectral correlations and synthesis of multidimensional fractional Brownian motion

Fractional Brownian motions (fBm) provide important models for a wide range of physical phenomena whose empirical spectra obey power laws of fractional order. Extensions of fBm to higher dimension has become increasingly important. In this paper we study isotropic d-dimensional fBm in the framework of inhomogeneous random fields, and we derive exact expressions for the dual-wavenumber spectrum of fractional Brownian fields (fBf). Based on the spectral correlation structure of fBf we develop an algorithm for synthesizing fBf. The proposed algorithm is accurate and allow us to generate fractional Brownian motions of arbitrary dimension.