The Exact Hausdorff Measure of the Zero Set of Certain Stationary Gaussian Processes
The Exact Hausdorff Measure of the Zero Set of Certain Stationary Gaussian Processes
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 $\Psi(h) = h^{1-\alpha}(\log |\log h|)^\alpha$.