On Strong Mixing Conditions for Stationary Gaussian Processes

A. N. Kolmogorov   ; Yu. A. Rozanov

Teoriâ veroâtnostej i ee primeneniâ, Tome 5 (1960) no. 2, pp. 222-227

Résumé

This paper considers conditions, which guarantee strong mixing of stationary random Gaussian process $\xi (t)$. It is proved, for example, that if the spectral density $f(\lambda)$ of the process $\xi(t)$ is continuous and positive (parameter $t$ is discrete) or $f(\lambda )$ is positive and uniformly continuous, and for large $\lambda$ $$\frac{m}{\lambda^k}\leq f(\lambda)\leq\frac{M}{\lambda^{k-1}}$$ (parameter $t$ is continuous), then strong mixing takes place.