The Annals of Probability

Some Local Properties of Gaussian Vector Fields

Jack Cuzick

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Abstract

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.

Article information

Source
Ann. Probab., Volume 6, Number 6 (1978), 984-994.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995388

Digital Object Identifier
doi:10.1214/aop/1176995388

Mathematical Reviews number (MathSciNet)
MR512415

Zentralblatt MATH identifier
0395.60038

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G17: Sample path properties

Keywords
Gaussian vector fields level sets Hausdorff dimension capacity local time

Citation

Cuzick, Jack. Some Local Properties of Gaussian Vector Fields. Ann. Probab. 6 (1978), no. 6, 984--994. doi:10.1214/aop/1176995388. https://projecteuclid.org/euclid.aop/1176995388


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