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JOURNALS // Teoriya Veroyatnostei i ee Primeneniya // Archive

Teor. Veroyatnost. i Primenen., 1963 Volume 8, Issue 2, Pages 184–189 (Mi tvp4661)

This article is cited in 105 papers

Short Communications

Periodically and Almost Periodically Correlated Random Processes with a Continuous Parameter

E. G. Gladyšev

Institute of Atmospheric Physics, USSR Academy of Sciences

Abstract: The random process $x(t),\infty<t<\infty$, with ${\mathbf M}x(t)={\mathbf M}x(t+t_0),\quad{\mathbf M}x(s)\overline{x(t)}={\mathbf M}x(s+t_0)\overline{x(t+t_0)}$ for fixed ${t_0}$ is called periodically correlated. Almost periodically correlated processes are defined by analogy.
The property of positive definiteness of covariation and the harmonizability of these processes are considered.

Received: 02.10.1961


 English version:
Theory of Probability and its Applications, 1963, 8:2, 173–177


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