Local stationarity and simulation of self-affine intrinsic random functions

Gaussian intrinsic random functions with power law generalized covariance functions, which in one dimension essentially correspond to fractional and integrated fractional Brownian motions, form a class of self-affine models for random fields with a wide range of smoothness properties. These random fields are nonstationary, but appropriately filtered versions of them are stationary. This work proves that most such random functions are locally stationary in a certain well-defined sense. This result yields an efficient and exact method of simulating all fractional and integrated fractional Brownian motions.