Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part VI, Tome 97 (1980), pp. 32-44
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V. V. Gorodestkii. The invariance principle for functions of stationary Gaussian variables. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part VI, Tome 97 (1980), pp. 32-44. http://geodesic.mathdoc.fr/item/ZNSL_1980_97_a4/
@article{ZNSL_1980_97_a4,
author = {V. V. Gorodestkii},
title = {The invariance principle for functions of stationary {Gaussian} variables},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {32--44},
year = {1980},
volume = {97},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1980_97_a4/}
}
TY - JOUR
AU - V. V. Gorodestkii
TI - The invariance principle for functions of stationary Gaussian variables
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1980
SP - 32
EP - 44
VL - 97
UR - http://geodesic.mathdoc.fr/item/ZNSL_1980_97_a4/
LA - ru
ID - ZNSL_1980_97_a4
ER -
%0 Journal Article
%A V. V. Gorodestkii
%T The invariance principle for functions of stationary Gaussian variables
%J Zapiski Nauchnykh Seminarov POMI
%D 1980
%P 32-44
%V 97
%U http://geodesic.mathdoc.fr/item/ZNSL_1980_97_a4/
%G ru
%F ZNSL_1980_97_a4
Let $\{Y_j\}$ – the stationary Gaussian sequence. $$ G(x)\in L^2\biggl(R^1,\frac1{\sqrt{2\pi}}e^{-x^2/2}\,dx\biggl),\quad X_j=G(Y_j). $$ The invariance principle for $\{X_j\}$ is proved. The representation of limiting process as the stochastic integral is obtained too.
