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.
@article{VMUMM_2023_6_a5,
author = {V. I. Piterbarg},
title = {Asymptotic behavior of point processes of exits of a {Gaussian} stationary sequence beyond high levels},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {36--42},
publisher = {mathdoc},
number = {6},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a5/}
}
TY - JOUR AU - V. I. Piterbarg TI - Asymptotic behavior of point processes of exits of a Gaussian stationary sequence beyond high levels JO - Vestnik Moskovskogo universiteta. Matematika, mehanika PY - 2023 SP - 36 EP - 42 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a5/ LA - ru ID - VMUMM_2023_6_a5 ER -
%0 Journal Article %A V. I. Piterbarg %T Asymptotic behavior of point processes of exits of a Gaussian stationary sequence beyond high levels %J Vestnik Moskovskogo universiteta. Matematika, mehanika %D 2023 %P 36-42 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a5/ %G ru %F VMUMM_2023_6_a5
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/