Local stationarity and simulation of self-affine intrinsic random functions

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