Representations of isotropic Gaussian random fields with homogeneous increments

Abstract

We present series expansions and moving average representations of isotropic Gaussian random fields with homogeneous increments, making use of concepts of the theory of vibrating strings. We illustrate our results using the example of Lévy’s fractional Brownian motion on R N. Copyright © 2006 Kacha Dzhaparidze et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1