| Abstract: | Fractional Brownian surfaces are commonly used as models for landscapes and other physical processes in space. This work shows how to simulate fractional Brownian surfaces on a grid efficiently and exactly by embedding them in a periodic Gaussian random field and using the fast Fourier transform. Periodic embeddings are given that are proven to yield positive definite covariance functions and hence yield exact simulations for all possible densities of the simulation grid. Numerical results show these embeddings can sometimes be made more efficient in practice. Further numerical results show how the ideas developed for simulating fractional Brownian surfaces can be used for simulating other Gaussian random fields. The simulation methodology is used to study the behavior of a simple estimator of the parameters of a fractional Brownian surface. |
