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 $\Psi(h) = h^{1-\alpha}(\log |\log h|)^\alpha$.
Publié le : 1977-10-14
Classification:
Stationary Gaussian processes,
zero set,
Hausdorff measure,
exact measure function,
60G10,
60G15,
60G17,
60G25
@article{1176995716,
author = {Davies, P. Laurie},
title = {The Exact Hausdorff Measure of the Zero Set of Certain Stationary Gaussian Processes},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 740-755},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995716}
}
Davies, P. Laurie. The Exact Hausdorff Measure of the Zero Set of Certain Stationary Gaussian Processes. Ann. Probab., Tome 5 (1977) no. 6, pp. 740-755. http://gdmltest.u-ga.fr/item/1176995716/