Geodesic
Asymptotic behavior of point processes of exits of a Gaussian stationary sequence beyond high levels
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2023), pp. 36-42
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We study the asymptotic behavior of point processes of exits of a Gaussian stationary sequence beyond a level tending to infinity more slowly than in the Poisson limit theorem for the number of exits. Convergence in variation of such point processes to a marked Poisson process is proved. The results of Yu. V. Prokhorov on the best approximation of the Bernoulli distribution by a mixture of Gaussian and Poisson distributions are applied. A. N. Kolmogorov proposed this problem in the early 1950s. 
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V. I. Piterbarg. Asymptotic behavior of point processes of exits of a Gaussian stationary sequence beyond high levels. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2023), pp. 36-42. http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a5/

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