Polar Functions for Anisotropic Gaussian Random Fields

Zhenlong Chen

Abstract and Applied Analysis, 2014, vol. 2014, 1-18

Abstract:

Let X be an ( N , d )-anisotropic Gaussian random field. Under some general conditions on X , we establish a relationship between a class of continuous functions satisfying the Lipschitz condition and a class of polar functions of X . We prove upper and lower bounds for the intersection probability for a nonpolar function and X in terms of Hausdorff measure and capacity, respectively. We also determine the Hausdorff and packing dimensions of the times set for a nonpolar function intersecting X . The class of Gaussian random fields that satisfy our conditions includes not only fractional Brownian motion and the Brownian sheet, but also such anisotropic fields as fractional Brownian sheets, solutions to stochastic heat equation driven by space-time white noise, and the operator-scaling Gaussian random field with stationary increments.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2014/947171.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2014/947171.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:947171

DOI: 10.1155/2014/947171

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().