Geodesic
The exact asymptotics for the probability of large span of a~Gaussian stationary process
Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 3, pp. 480-495

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We obtain the exact asymptotics for the probability $$ \mathbf P\{\max_{0\le t\le 1}\xi_t-\min_{0\le t\le 1}\xi_t>u\},\qquad u\to\infty, $$ under the assumption that the correlation function of a Gaussian stationary process $\xi_t$, $t\in[0,1]$, varies regularly at the origin. 
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     author = {V. I. Piterbarg and V. P. Prisya\v{z}nuk},
     title = {The exact asymptotics for the probability of large span of {a~Gaussian} stationary process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {480--495},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a2/}
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V. I. Piterbarg; V. P. Prisyažnuk. The exact asymptotics for the probability of large span of a~Gaussian stationary process. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 3, pp. 480-495. http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a2/