Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 358-364
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V. V. Gorodeсkiǐ. The invariance principle for stationary random fields satisfying the strong mixing condition. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 358-364. http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a18/
@article{TVP_1982_27_2_a18,
author = {V. V. Gorode{\cyrs}kiǐ},
title = {The invariance principle for stationary random fields satisfying the strong mixing condition},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {358--364},
year = {1982},
volume = {27},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a18/}
}
TY - JOUR
AU - V. V. Gorodeсkiǐ
TI - The invariance principle for stationary random fields satisfying the strong mixing condition
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1982
SP - 358
EP - 364
VL - 27
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a18/
LA - ru
ID - TVP_1982_27_2_a18
ER -
%0 Journal Article
%A V. V. Gorodeсkiǐ
%T The invariance principle for stationary random fields satisfying the strong mixing condition
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1982
%P 358-364
%V 27
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a18/
%G ru
%F TVP_1982_27_2_a18
Let $\xi(u)$, $u\in R^q$, be a stationary random field satisfying the strong mixing condition, $V$ be an open set in $R^q$ with finite Lebesgue's measure $\mu(V)$, $$ T(V)=\int_V\xi(u)\,du, $$ The sufficient condition for the weak convergence of $$ \zeta_r(t)=(r^q\mu(V))^{-1/2}T(rt^{1/q}V),\qquad t\in[0,1], $$ to some Gaussian process $w_V(t)$ are obtained.
