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Teor. Veroyatnost. i Primenen., 1965, Volume 10, Issue 2, Pages 386–389 (Mi tvp536)  

Short Communications

On the maximum of a Gaussian stationary process

M. G. Šur

Moscow

Abstract: 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 $\sigma^2=\mathbf Mx^2(t)$.

Full text: PDF file (261 kB)

English version:
Theory of Probability and its Applications, 1965, 10:2, 354–357

Bibliographic databases:

Received: 07.10.1964

Citation: M. G. Šur, “On the maximum of a Gaussian stationary process”, Teor. Veroyatnost. i Primenen., 10:2 (1965), 386–389; Theory Probab. Appl., 10:2 (1965), 354–357

Citation in format AMSBIB
\Bibitem{Shu65}
\by M.~G.~{\v S}ur
\paper On the maximum of a~Gaussian stationary process
\jour Teor. Veroyatnost. i Primenen.
\yr 1965
\vol 10
\issue 2
\pages 386--389
\mathnet{http://mi.mathnet.ru/tvp536}
\zmath{https://zbmath.org/?q=an:0137.35602}
\transl
\jour Theory Probab. Appl.
\yr 1965
\vol 10
\issue 2
\pages 354--357
\crossref{https://doi.org/10.1137/1110044}


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