87
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Spatial and Spatiotemporal Karhunen-Loève-Type Representations on Fractal Domains

, &
Pages 195-219 | Received 12 Jan 2005, Accepted 31 Mar 2005, Published online: 15 Feb 2007
 

Abstract

We study the spectral properties of spatial and spatiotemporal Gaussian random fields defined as the solutions to stochastic elliptic, parabolic, and hyperbolic fractional pseudodifferential equations on compact fractal domains. The fractal dimension of the domain modifies the asymptotic properties of the eigenvalues that define the pure point spectra of the covariance functions of the solutions and their Karhunen-Loève-type expansions. The eigenfunction systems involved constitute orthogonal bases of the corresponding trace spaces on fractal sets. The Hölder exponent of the sample paths of the random fields is computed in terms of the fractional order of mean-quadratic variation on their increments. Such an exponent also depends on the Hausdorff dimension of the domain.

Mathematics Subject Classification:

ACKNOWLEDGMENT

This work is partially supported by project BFM2002-01836 of the DGI, Spain, and by the Australian Research Council grants LX0348297 and DP0559807.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.