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JOURNALS // Teoriya Veroyatnostei i ee Primeneniya // Archive

Teor. Veroyatnost. i Primenen., 1960 Volume 5, Issue 2, Pages 222–227 (Mi tvp4828)

This article is cited in 214 papers

Short Communications

On Strong Mixing Conditions for Stationary Gaussian Processes

A. N. Kolmogorov, Yu. A. Rozanov

Moscow

Abstract: 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.

Received: 18.11.1959


 English version:
Theory of Probability and its Applications, 1960, 5:2, 204–208


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