Geodesic
On the maximum of a Gaussian stationary process
Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 2, pp. 386-389 
M. G. Šur. On the maximum of a Gaussian stationary process. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 2, pp. 386-389. http://geodesic.mathdoc.fr/item/TVP_1965_10_2_a18/
@article{TVP_1965_10_2_a18,
     author = {M. G. \v{S}ur},
     title = {On the maximum of {a~Gaussian} stationary process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {386--389},
     year = {1965},
     volume = {10},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_2_a18/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a Gaussian real process $x(t)$ which satisfies the same conditions as in [1]. We prove the existence (a.s.) of such random number $t_0$ ($t_0<\infty$) that the inequality $$ |\max_{o\le u\le t}x(u)-\sigma\sqrt{2\ln t}|<\frac{(\sigma+\varepsilon)\ln\ln t}{\sqrt{2\ln t}} $$ is valid for all $t>t_0$ where $\varepsilon$ is any fixed positive number and $\sigma^2=\mathbf Mx^2(t)$.