Polar Functions for Anisotropic Gaussian Random Fields
Author
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-03-23
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Chen, Zhenlong. 2014. Polar Functions for Anisotropic Gaussian Random Fields. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-18.
https://search.emarefa.net/detail/BIM-1015122
Modern Language Association (MLA)
Chen, Zhenlong. Polar Functions for Anisotropic Gaussian Random Fields. Abstract and Applied Analysis No. 2014 (2014), pp.1-18.
https://search.emarefa.net/detail/BIM-1015122
American Medical Association (AMA)
Chen, Zhenlong. Polar Functions for Anisotropic Gaussian Random Fields. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-18.
https://search.emarefa.net/detail/BIM-1015122
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1015122