GENERALIZED SPECTRAL-ANALYSIS OF FRACTIONAL RANDOM-FIELDS

This paper considers a large class of non-stationary random fields whi ch have fractal characteristics and may exhibit long-range dependence. Its motivation comes from a Lipschitz-Holder-type condition in the sp ectral domain. The paper develops a spectral theory for the random fie lds, including a spectral decomposition, a covariance representation a nd a fractal index. From the covariance representation, the covariance function and spectral density of these fields are defined. These conc epts are useful in multiscaling analysis of random fields with long-ra nge dependence.