Geodesic
Properties of Sample Functions of a Stationary Gaussian Process
Teoriâ veroâtnostej i ee primeneniâ, Tome 5 (1960) no. 1, pp. 132-134 
R. L. Dobrushin. Properties of Sample Functions of a Stationary Gaussian Process. Teoriâ veroâtnostej i ee primeneniâ, Tome 5 (1960) no. 1, pp. 132-134. http://geodesic.mathdoc.fr/item/TVP_1960_5_1_a11/
@article{TVP_1960_5_1_a11,
     author = {R. L. Dobrushin},
     title = {Properties of {Sample} {Functions} of a {Stationary} {Gaussian} {Process}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {132--134},
     year = {1960},
     volume = {5},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1960_5_1_a11/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\{\xi_t(\omega),-\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.