An Asymptotic 0-1 Behavior of Gaussian Processes
An Asymptotic 0-1 Behavior of Gaussian Processes
Let $\{X(t), -\infty < t < \infty\}$ be a stationary Gaussian process with covariance function satisfying: (1) $r(t) = 1 - C|t|^\alpha + o(|t|^\alpha)$ as $t \rightarrow 0: C > 0, 0 < \alpha \leqq 2$; and (2) $r(t) = O(t^{-\gamma})$ as $t \rightarrow \infty: \gamma > 0$. Then for …