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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1960, Volume 5, Issue 1, Pages 132–134 (Mi tvp4820)

Short Communications

Properties of Sample Functions of a Stationary Gaussian Process

R. L. Dobrushin

Moscow

Abstract: Let $\{\xi_t(\omega),-\infty<t<\infty\}$ be a separable stationary Gaussian process with a continuous correlation function. Then, the following alternative holds true:
1) either for almost all w the sample functions of the process $\xi_t(\omega)$ are continuous functions of $t$.
2) or there exists a $\beta>0$ such that for almost all $\omega$ the sample function $\xi_t(\omega)$ is such that
$$\varlimsup_{t\to t_0}\xi_t(\omega)-\varliminf_{t\to t_0}\xi_t(\omega)\geq\beta$$
for any $t_0$.
In the second case almost all sample functions have no points of first order discontinuities.

Full text: PDF file (410 kB)

English version:
Theory of Probability and its Applications, 1960, 5:1, 120–122

Citation: R. L. Dobrushin, “Properties of Sample Functions of a Stationary Gaussian Process”, Teor. Veroyatnost. i Primenen., 5:1 (1960), 132–134; Theory Probab. Appl., 5:1 (1960), 120–122

Citation in format AMSBIB
\Bibitem{Dob60} \by R.~L.~Dobrushin \paper Properties of Sample Functions of a Stationary Gaussian Process \jour Teor. Veroyatnost. i Primenen. \yr 1960 \vol 5 \issue 1 \pages 132--134 \mathnet{http://mi.mathnet.ru/tvp4820} \transl \jour Theory Probab. Appl. \yr 1960 \vol 5 \issue 1 \pages 120--122 \crossref{https://doi.org/10.1137/1105012}