Open Access
2014 Polar Functions for Anisotropic Gaussian Random Fields
Zhenlong Chen
Abstr. Appl. Anal. 2014(SI35): 1-18 (2014). DOI: 10.1155/2014/947171


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.


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Zhenlong Chen. "Polar Functions for Anisotropic Gaussian Random Fields." Abstr. Appl. Anal. 2014 (SI35) 1 - 18, 2014.


Published: 2014
First available in Project Euclid: 6 October 2014

MathSciNet: MR3191078
Digital Object Identifier: 10.1155/2014/947171

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI35 • 2014
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