On the upper and lower classes for a stationary Gaussian stochastic process
Real stationary standardized Gaussian random fields (r.f.s) \(\xi(t, \omega)\) on a pseudometric unbounded space \((T,\rho)\) are considered under some rather mild conditions on the correlation function. An integral criterion is obtained for the zero-one law of the set \[ \{\omega: \text{ the set } \{t\in T:\;\xi(t,\omega)> \psi(t)\} \text{ is \(\rho\)-unbounded}\} \] when the function \(\psi: T\to [-\infty, +\infty]\) is not required to be monotone. In particular, the r.f.s of this type and the Brownian sheet are discussed when \(T= R^ n\) and two examples of r.f.s with \(T\) non-Euclidean are presented.
scientific article; zbMATH DE number 567174