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October, 1977 The Exact Hausdorff Measure of the Zero Set of Certain Stationary Gaussian Processes
P. Laurie Davies
Ann. Probab. 5(5): 740-755 (October, 1977). DOI: 10.1214/aop/1176995716

Abstract

It is shown that the exact measure function $\Psi(h)$ of a stationary Gaussian process with spectral density function $f(\lambda)$ proportional to $(\lambda^2 + a^2)^{-(\alpha+\frac{1}{2})}, 0 < \alpha < \frac{1}{2}$, is given by $\Psi(h) = h^{1-\alpha}(\log |\log h|)^\alpha$.

Citation

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P. Laurie Davies. "The Exact Hausdorff Measure of the Zero Set of Certain Stationary Gaussian Processes." Ann. Probab. 5 (5) 740 - 755, October, 1977. https://doi.org/10.1214/aop/1176995716

Information

Published: October, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0375.60043
MathSciNet: MR443053
Digital Object Identifier: 10.1214/aop/1176995716

Subjects:
Primary: 60G10
Secondary: 60G15, 60G17, 60G25

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 5 • October, 1977
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