Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 1, pp. 185-189
Citer cet article
V. I. Piterbarg. The central limit theorem for the number of level crossings of a stationary Gaussian process. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 1, pp. 185-189. http://geodesic.mathdoc.fr/item/TVP_1978_23_1_a17/
@article{TVP_1978_23_1_a17,
author = {V. I. Piterbarg},
title = {The central limit theorem for the number of level crossings of a~stationary {Gaussian} process},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {185--189},
year = {1978},
volume = {23},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_1_a17/}
}
TY - JOUR
AU - V. I. Piterbarg
TI - The central limit theorem for the number of level crossings of a stationary Gaussian process
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1978
SP - 185
EP - 189
VL - 23
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1978_23_1_a17/
LA - ru
ID - TVP_1978_23_1_a17
ER -
%0 Journal Article
%A V. I. Piterbarg
%T The central limit theorem for the number of level crossings of a stationary Gaussian process
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1978
%P 185-189
%V 23
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1978_23_1_a17/
%G ru
%F TVP_1978_23_1_a17
Let $r(t)$ be the covariance function of a stationary Gaussian process with zero mean. If $$ \int_0^{\infty}t(|r(t)|+|r'(t)|+|r''(t)|)\,dt<\infty, $$ then the central limit theorem for the number of level crossings in a large interval is proved to hold.
