This article is cited in 5 papers

Short Communications

n the Unboundedness of the Sample Functions of Gaussian Processes

Yu. K. Belyaev

Moscow

Abstract: The following theorem is proved: if $x(t)$ is a stationary separable gaussian random process whose spectral function has a non-null continuous component, then almost all sample functions of this process are unbounded.

Received: 09.01.1958

 English version: Theory of Probability and its Applications, 1958, 3:3, 327–329