Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 2, pp. 370-372
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Yu. M. Ryzhov. Limit Theorems for Functionals of Sample Functions of a Stationary Gaussian Process. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 2, pp. 370-372. http://geodesic.mathdoc.fr/item/TVP_1967_12_2_a14/
@article{TVP_1967_12_2_a14,
author = {Yu. M. Ryzhov},
title = {Limit {Theorems} for {Functionals} of {Sample} {Functions} of {a~Stationary} {Gaussian} {Process}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {370--372},
year = {1967},
volume = {12},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_2_a14/}
}
TY - JOUR
AU - Yu. M. Ryzhov
TI - Limit Theorems for Functionals of Sample Functions of a Stationary Gaussian Process
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1967
SP - 370
EP - 372
VL - 12
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1967_12_2_a14/
LA - ru
ID - TVP_1967_12_2_a14
ER -
%0 Journal Article
%A Yu. M. Ryzhov
%T Limit Theorems for Functionals of Sample Functions of a Stationary Gaussian Process
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1967
%P 370-372
%V 12
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1967_12_2_a14/
%G ru
%F TVP_1967_12_2_a14
Let $\xi(t)$, $t\in[0,T]$, be a stationary Gaussian process with zero mean. We investigate the conditions for the functionals $$ S_n=\sum_{k=1}^nf_n\biggl(\xi\biggl(\frac knT\biggr)\biggr)\frac Tn $$ to converge to the additive functionals $$ J=\int_0^Tg(\xi(t))\,dt. $$
