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December, 1978 Some Local Properties of Gaussian Vector Fields
Jack Cuzick
Ann. Probab. 6(6): 984-994 (December, 1978). DOI: 10.1214/aop/1176995388


Formulas for the Hausdorff dimension of the graph, image, and level sets of Gaussian vector fields are given under general conditions which allow for different local behavior of the components and for dependence among them. Conditions for the field to have a local time, to hit any fixed point, and for the image to have positive Lebesgue measure are given, and relations between these properties are discussed. Applications of the results are given and include a discussion of when differentiable planar fields have critical points at fixed levels.


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Jack Cuzick. "Some Local Properties of Gaussian Vector Fields." Ann. Probab. 6 (6) 984 - 994, December, 1978.


Published: December, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0395.60038
MathSciNet: MR512415
Digital Object Identifier: 10.1214/aop/1176995388

Primary: 60G15
Secondary: 60G17

Keywords: capacity , Gaussian vector fields , Hausdorff dimension , Level sets , Local time

Rights: Copyright © 1978 Institute of Mathematical Statistics

Vol.6 • No. 6 • December, 1978
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