Geodesic
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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@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},
     publisher = {mathdoc},
     volume = {97},
     year = {1980},
     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
PB  - mathdoc
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
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_1980_97_a4/
%G ru
%F ZNSL_1980_97_a4
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/