Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 72731, 25 pages
doi:10.1155/JAMSA/2006/72731

Representations of isotropic Gaussian random fields with homogeneous increments

Kacha Dzhaparidze,1 Harry van Zanten,2 and Pawel Zareba2

1Department PNA, Center for Mathematics and Computer Science, Kruislaan 413, Amsterdam 1098 SJ, The Netherlands
2Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081a, Amsterdam 1081 HV, The Netherlands

Received 13 December 2005; Revised 10 May 2006; Accepted 8 June 2006

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.

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 ℝN.